Rs Aggarwal Solutions for Class 6 Math Chapter 1 Number System are provided here with simple step-by-step explanations. These solutions for Number System are extremely popular among Class 6 students for Math Number System Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal Book of Class 6 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal Solutions. All Rs Aggarwal Solutions for class Class 6 Math are prepared by experts and are 100% accurate.

#### Page No 113:

#### Question 1:

Write each of the following in figures:

(i) Fifty-eight point six three

(ii) One hundred twenty-four point four two five

(iii) Seven point seven six

(iv) Nineteen point eight

(v) Four hundred four point zero four four

(vi) Point one seven three

(vii) Point zero one five

#### Answer:

(i) 58.63

(ii) 124.425

(iii) 7.76

(iv) 19.8

(v) 404.044

(vi) 0.173

(vii) 0.015

#### Page No 113:

#### Question 2:

Write the place value of each digit in each of the following decimals:

(i) 14.83

(ii) 275.269

(iii) 46.075

(iv) 302.459

(v) 5370.34

(vi) 186.209

#### Answer:

(i) In 14.83, we have:

Place value of 1 = 1 tens = 10

Place value of 4 = 4 ones = 4

Place value of 8 = 8 tenths = $\frac{8}{10}$

Place value of 3 = 3 hundredths = $\frac{3}{100}$

(ii) In 275.269, we have:

Place value of 2 = 2 hundreds = 200

Place value of 7 = 7 tens = 70

Place value of 5 = 5 ones = 5

Place value of 2 = 2 tenths = $\frac{2}{10}$

Place value of 6 = 6 hundredths = $\frac{6}{100}$

Place value of 9 = 9 thousandths = $\frac{9}{1000}$

(iii) In 46.075, we have:

Place value of 4 = 4 tens = 40

Place value of 6 = 6 ones = 6

Place value of 0 = 0 tenths = $\frac{0}{10}$= 0

Place value of 7 = 7 hundredths = $\frac{7}{100}$

Place value of 5 = 5 thousandths = $\frac{5}{1000}$

(iv) In 302.459, we have:

Place value of 3 = 3 hundreds = 300

Place value of 0 = 0 tens = 0

Place value of 2 = 2 ones = 2

Place value of 4 = 4 tenths = $\frac{4}{10}$

Place value of 5 = 5 hundredths = $\frac{5}{100}$

Place value of 9 = 9 thousandths = $\frac{9}{1000}$

(v) In 5370.34, we have:

Place value of 5 = 5 thousands = 5000

Place value of 3 = 3 hundreds = 300

Place value of 7 = 7 tens = 70

Place value of 0 = 0 ones = 0

Place value of 3 = 3 tenths = $\frac{3}{10}$

Place value of 4 = 4 hundredths = $\frac{4}{100}$

(vi) In 186.209, we have:

Place value of 1 = 1 hundreds = 100

Place value of 8 = 8 tens = 80

Place value of 6 = 6 ones = 6

Place value of 2 = 2 tenths = $\frac{2}{10}$

Place value of 0 = 0 hundredths = 0

Place value of 9 = 9 thousandths = $\frac{9}{1000}$

#### Page No 113:

#### Question 3:

Write each of the following decimals in expanded form:

(i) 67.83

(ii) 283.61

(iii) 24.675

(iv) 0.294

(v) 8.006

(vi) 4615.72

#### Answer:

(i) 67.83

= 6 tens + 7 ones + 8 tenths + 3 hundredths

= $60+7+\frac{8}{10}+\frac{3}{100}$

(ii) 283.61

= 2 hundreds + 8 tens + 3 ones + 6 tenths + 1 hundredths

= $200+80+3+\frac{6}{10}+\frac{1}{100}$

(iii) 24.675

= 2 tens + 4 ones + 6 tenths + 7 hundredths + 5 thousandths

= $20+4+\frac{6}{10}+\frac{7}{100}+\frac{5}{1000}$

(iv) 0.294

= 2 tenths + 9 hundredths + 4 thousandths

= $\frac{2}{10}+\frac{9}{100}+\frac{4}{1000}$

(v) 8.006

= 8 ones + 0 tenths + 0 hundredths + 6 thousandths

= $8+\frac{0}{10}+\frac{0}{100}+\frac{6}{1000}$

(vi) 4615.72

= 4 thousands + 6 hundreds + 1 tens + 5 ones + 7 tenths + 2 hundredths

= $4000+600+10+5+\frac{7}{10}+\frac{2}{100}$

#### Page No 113:

#### Question 4:

Write each of the following in decimals form:

(i) $40+6+\frac{7}{10}+\frac{9}{100}$

(ii) $500+70+8+\frac{3}{10}+\frac{1}{100}+\frac{6}{1000}$

(iii) $700+30+1+\frac{8}{10}+\frac{4}{100}$

(iv) $600+5+\frac{7}{100}+\frac{9}{1000}$

(v) $800+5+\frac{8}{10}+\frac{6}{1000}$

(vi) $30+9+\frac{4}{100}+\frac{8}{1000}$

#### Answer:

(i) $40+6+\frac{7}{10}+\frac{9}{100}$ = 46 + 0.7 + .09 = 46.79

(ii) $500+70+8+\frac{3}{10}+\frac{1}{100}+\frac{6}{1000}$ = 578 + 0.3 + 0.01 + 0.006 = 578.316

(iii) $700+30+1+\frac{8}{10}+\frac{4}{100}$ = 731 + 0.8 + 0.04 = 731.84

(iv) $600+5+\frac{7}{100}+\frac{9}{1000}$ = 605 + 0.07 + 0.009 = 605.079

(v) $800+5+\frac{8}{10}+\frac{6}{1000}$ = 805 + 0.8 + 0.006 = 805.806

(vi) $30+9+\frac{4}{100}+\frac{8}{1000}$ = 39 + 0.04 + 0.008 = 39.048

#### Page No 114:

#### Question 5:

Convert each of the following into like decimals:

(i) 7.5, 64.23, 0.074

(ii) 0.6, 5.937, 2.36, 4.2

(iii) 1.6, 0.07, 3.58, 2.9

(iv) 2.5, 0.63, 14.08, 1.637

#### Answer:

(i) Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

7.5 = 7.500

64.23 = 64.230

0.074 = 0.074

(ii) Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

0.6 = 0.600

5.937 = 5.937

2.36 = 2.360

4.2 = 4.200

(iii) Each of the numbers has maximum 2 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

1.6 = 1.60

0.07 = 0.07

3.58 = 3.58

2.9 = 2.90

(iv) Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

2.5 = 2.500

0.63 = 0.630

14.08 = 14.080

1.637 = 1.637

#### Page No 114:

#### Question 6:

Fill in each of the place holders with the correct symbol > or <:

(i) $84.23\overline{)}76.35$

(ii) $7.608\overline{)}7.68$

(iii) $8.34\overline{)}8.43$

(iv) $12.06\overline{)}12.006$

(v) $3.85\overline{)}3.805$

(vi) $0.97\overline{)}1.07$

#### Answer:

(i) 84.23 > 76.35

Since 84 is greater than 76, 84.23 is greater than 76.35. (Comparing the whole number parts)

(ii) 7.608 < 7.680

Since 8 is greater than 0 at the hundredths place, 7.608 is smaller than 7.680.

(iii) 8.34 < 8.43

Since 4 is greater than 3 at the tenths place, 8.34 is smaller than 8.43.

(iv) 12.06 > 12.006

Since 6 is greater than 0 at the hundredths place, 12.06 is greater than 12.006.

(v) 3.850 > 3.805

Since 5 is greater than 0 at the hundredths place, 3.850 is greater than 3.805.

(vi) 0.97 < 1.07

Since 1 is greater than 0, 0.97 is smaller than 1.07. (Comparing the whole number parts)

#### Page No 114:

#### Question 7:

Arrange the following decimals in ascending order:

(i) 5.8, 7.2, 5.69, 7.14, 5.06

(ii) 0.6, 6.6, 6.06, 66.6, 0.06

(iii) 6.54, 6.45, 6.4, 6.5, 6.05

(iv) 3.3, 3.303, 3.033, 0.33, 3.003

#### Answer:

(i) 5.8, 7.2, 5.69, 7.14, 5.06

Converting the given decimals into like decimals:

5.80, 7.20, 5.69, 7.14, 5.06

Clearly, 5.06 < 5.69 < 5.80 < 7.14 < 7.20

Hence, the given decimals can be arranged in the ascending order as follows:

5.06, 5.69, 5.80, 7.14 and 7.2

(ii) 0.6, 6.6, 6.06, 66.6, 0.06

Converting the given decimals into like decimals:

0.60, 6.60, 6.06, 66.60, 0.06

Clearly, 0.06 < 0.60 < 6.06 < 6.60 < 66.60

Hence, the given decimals can be arranged in the ascending order as follows:

0.06, 0.60, 6.06, 6.60 and 66.60

(iii) 6.54, 6.45, 6.4, 6.5, 6.05

Converting the given decimals into like decimals:

6.54, 6.45, 6.40, 6.50, 6.05

Clearly, 6.05 < 6.40 < 6.45 < 6.50 < 6.54

Hence, the given decimals can be arranged in the ascending order as follows:

6.05, 6.40, 6.45, 6.50 and 6.54

(iv) 3.3, 3.303, 3.033, 0.33, 3.003

Converting the given decimals into like decimals:

3.300, 3.303, 3.033, 0.330, 3.003

Clearly, 0.330 < 3.003 < 3.033 < 3.300 < 3.303

Hence, the given decimals can be arranged in the ascending order as follows:

0.33, 3.003, 3.033, 3.300 and 3.303

#### Page No 114:

#### Question 8:

Arrange the following decimals in descending order:

(i) 7.3, 8.73, 73.03, 7.33, 8.073

(ii) 3.3, 3.03, 30.3, 30.03, 3.003

(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007

(iv) 8.88, 8.088, 88.8, 88.08, 8.008

#### Answer:

(i) 7.3, 8.73, 73.03, 7.33, 8.073

Converting each decimal into like decimals:

7.300, 8.730, 73.030, 7.330, 8.073

Clearly, 73.030 > 8.730 > 8.073 > 7.330 > 7.300

Hence, the given decimals can be arranged in the descending order as follows:

73.03, 8.73, 8.073, 7.33 and 7.3

(ii) 3.3, 3.03, 30.3, 30.03, 3.003

Converting each decimal into like decimals:

3.300, 3.030, 30.300, 30.030, 3.003

Clearly, 30.300 > 30.030 > 3.300 > 3.030 > 3.003

Hence, the given decimals can be arranged in the descending order as follows:

30.3, 30.03, 3.3, 3.03 and 3.003

(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007

Converting each decimal into like decimals:

2.700, 7.200, 2.270, 2.720, 2.020, 2.007

Clearly, 7.200 > 2.720 > 2.700 > 2.270 > 2.020 > 2.007

Hence, the given decimals can be arranged in the descending order as follows:

7.2, 2.72, 2.7, 2.27, 2.02 and 2.007

(iv) 8.88, 8.088, 88.8, 88.08, 8.008

Converting each decimal into like decimals:

8.880, 8.088, 88.800, 88.080, 8.008

Clearly, 88.800 > 88.080 > 8.880 > 8.088 > 8.008

Hence, the given decimals can be arranged in the descending order as follows:

88.8, 88.08, 8.88, 8.088 and 8.008

#### Page No 118:

#### Question 1:

*Convert each of the following into a fraction in its simplest form:*

.9

#### Answer:

We have:

.9 = $\frac{9}{10}$

#### Page No 118:

#### Question 2:

*Convert each of the following into a fraction in its simplest form:*

0.6

#### Answer:

We have:

0.6 = $\frac{6}{10}=\frac{3}{5}$

#### Page No 118:

#### Question 3:

*Convert each of the following into a fraction in its simplest form:*

.08

#### Answer:

We have:

0.08 = $\frac{8}{100}=\frac{4}{50}=\frac{2}{25}$

#### Page No 118:

#### Question 4:

*Convert each of the following into a fraction in its simplest form:*

0.15

#### Answer:

We have:

0.15 = $\frac{15}{100}=\frac{3}{20}$

#### Page No 118:

#### Question 5:

*Convert each of the following into a fraction in its simplest form:*

0.48

#### Answer:

We have:

0.48 = $\frac{48}{100}=\frac{12}{25}$

#### Page No 118:

#### Question 6:

*Convert each of the following into a fraction in its simplest form:*

.053

#### Answer:

We have:

0.053 = $\frac{53}{1000}$

#### Page No 118:

#### Question 7:

*Convert each of the following into a fraction in its simplest form:*

0.125

#### Answer:

We have:

0.125 = $\frac{125}{1000}=\frac{25}{200}=\frac{5}{40}=\frac{1}{8}$

#### Page No 118:

#### Question 8:

*Convert each of the following into a fraction in its simplest form:*

.224

#### Answer:

We have:

0.224 = $\frac{224}{1000}=\frac{56}{250}=\frac{28}{125}$

#### Page No 118:

#### Question 9:

*Convert each of the following as a mixed-fraction:*

6.4

#### Answer:

We have:

6.4 = $\frac{64}{10}=\frac{32}{5}=6\frac{2}{5}$

#### Page No 118:

#### Question 10:

*Convert each of the following as a mixed-fraction:*

16.5

#### Answer:

We have:

16.5 = $\frac{165}{10}=\frac{33}{2}=16\frac{1}{2}$

#### Page No 118:

#### Question 11:

*Convert each of the following as a mixed-fraction:*

8.36

#### Answer:

We have:

8.36 = $\frac{836}{100}=\frac{209}{25}=8\frac{9}{25}$

#### Page No 118:

#### Question 12:

*Convert each of the following as a mixed-fraction:*

4.275

#### Answer:

We have:

4.275 = $\frac{4275}{1000}=\frac{171}{40}=4\frac{11}{40}$

#### Page No 118:

#### Question 13:

*Convert each of the following as a mixed-fraction:*

25.06

#### Answer:

We have:

25.06 = $\frac{2506}{100}=\frac{1253}{50}=25\frac{3}{50}$

#### Page No 118:

#### Question 14:

*Convert each of the following as a mixed-fraction:*

7.004

#### Answer:

We have:

7.004 = $\frac{7004}{1000}=\frac{1751}{250}=7\frac{1}{250}$

#### Page No 118:

#### Question 15:

*Convert each of the following as a mixed-fraction:*

2.052

#### Answer:

We have:

2.052 = $\frac{2052}{1000}=\frac{513}{250}=2\frac{13}{250}$

#### Page No 118:

#### Question 16:

*Convert each of the following as a mixed-fraction:*

3.108

#### Answer:

We have:

3.108 = $\frac{3108}{1000}=\frac{777}{250}=3\frac{27}{250}$

#### Page No 118:

#### Question 17:

*Convert each of the following into a decimal:*

$\frac{23}{10}$

#### Answer:

We have:

$\frac{23}{10}=2\frac{3}{10}=2+0.3=2.3$

#### Page No 118:

#### Question 18:

*Convert each of the following into a decimal:*

$\frac{167}{100}$

#### Answer:

We have:

$\frac{167}{100}=1\frac{67}{100}=1+0.67=1.67$

#### Page No 118:

#### Question 19:

*Convert each of the following into a decimal:*

$\frac{1589}{100}$

#### Answer:

We have:

$\frac{1589}{100}=15\frac{89}{100}=15+0.89=15.89$

#### Page No 118:

#### Question 20:

*Convert each of the following into a decimal:*

$\frac{5413}{1000}$

#### Answer:

We have:

$\frac{5413}{1000}=5\frac{413}{1000}=5+0.413=5.413$

#### Page No 118:

#### Question 21:

*Convert each of the following into a decimal:*

$\frac{21415}{1000}$

#### Answer:

We have:

$\frac{21415}{1000}=21\frac{415}{1000}=21+0.415=21.415$

#### Page No 118:

#### Question 22:

*Convert each of the following into a decimal:*

$\frac{25}{4}$

#### Answer:

We have:

$\frac{25}{4}=6\frac{1}{4}=6+0.25=6.25$

#### Page No 118:

#### Question 23:

*Convert each of the following into a decimal:*

$3\frac{3}{5}$

#### Answer:

We have:

$3\frac{3}{5}=3+0.6=3.6$

#### Page No 118:

#### Question 24:

*Convert each of the following into a decimal:*

$1\frac{4}{25}$

#### Answer:

We have:

$1\frac{4}{25}=1+0.16=1.16$

#### Page No 118:

#### Question 25:

*Convert each of the following into a decimal:*

$5\frac{17}{50}$

#### Answer:

We have:

$5\frac{17}{50}=5+0.34=5.34$

#### Page No 118:

#### Question 26:

*Convert each of the following into a decimal:*

$12\frac{3}{8}$

#### Answer:

We have:

$12\frac{3}{8}=12+0.375=12.375$

#### Page No 118:

#### Question 27:

*Convert each of the following into a decimal:*

$2\frac{19}{40}$

#### Answer:

We have:

$2\frac{19}{40}=2+0.475=2.475$

#### Page No 118:

#### Question 28:

*Convert each of the following into a decimal:*

$\frac{19}{20}$

#### Answer:

We have:

$\frac{19}{20}=0.95$

#### Page No 118:

#### Question 29:

*Convert each of the following into a decimal:*

$\frac{37}{50}$

#### Answer:

We have:

$\frac{37}{50}=0.74$

#### Page No 118:

#### Question 30:

*Convert each of the following into a decimal:*

$\frac{107}{250}$

#### Answer:

We have:

$\frac{107}{250}=0.428$

#### Page No 118:

#### Question 31:

*Convert each of the following into a decimal:*

$\frac{3}{40}$

#### Answer:

We have:

$\frac{3}{40}=0.075$

#### Page No 118:

#### Question 32:

*Convert each of the following into a decimal:*

$\frac{7}{8}$

#### Answer:

We have:

$\frac{7}{8}=0.875$

#### Page No 118:

#### Question 33:

Using decimals, express

(i) 8 kg 640 g in kilograms

(ii) 9 kg 37 g in kilograms

(iii) 6 kg 8 g in kilograms

#### Answer:

(i) 8 kg 640 g in kilograms:

8 kg + 640 gm = 8 kg + $\frac{640}{1000}$ kg

8 kg + 0.640 kg = 8.640 kg

(ii) 9 kg 37 g in kilograms:

9 kg + 37 gm = 9 kg + $\frac{37}{1000}$ kg

9 kg + 0.037 kg = 9.037 kg

(iii) 6 kg 8 g in kilograms:

6 kg + 8 gm = 6 kg + $\frac{8}{1000}$ kg

6 kg + 0.008 kg = 6.008 kg

#### Page No 118:

#### Question 34:

Using decimals, express

(i) 4 km 365 m in kilometres

(ii) 5 km 87 m in kilometres

(iii) 3 km 6 m in kilometres

(iv) 270 m in kilometres

(v) 35 m in kilometres

(vi) 6 m in kilometres

#### Answer:

(i) 4 km 365 m in kilometres:

4 km + 365 m = 4 km + $\frac{365}{1000}$ km [Since 1 km = 1000 m]

4 km + 0.365 km = 4.365 km

(ii) 5 km 87 m in kilometres:

5 km + 87 m = 5 km + $\frac{87}{1000}$ km [Since 1 km = 1000 m]

5 km + 0.087 km = 5.087 km

(iii) 3 km 6 m in kilometres:

3 km + 6 m = 3 km + $\frac{6}{1000}$ km [Since 1 km = 1000 m]

3 km + 0.006 km = 3.006 km

(iv) 270 m in kilometres:

$\frac{270}{1000}$ km = 0.270 km [Since 1 km = 1000 m]

(v) 35 m in kilometres:

$\frac{35}{1000}$ km = 0.035 km [Since 1 km = 1000 m]

(vi) 6 m in kilometres:

$\frac{6}{1000}$ km = 0.006 km [Since 1 km = 1000 m]

#### Page No 118:

#### Question 35:

Using decimals, express

(i) 15 kg 850 g in kilograms

(ii) 8 kg 96 g in kilograms

(iii) 540 g in kilograms

(iv) 8 g in kilograms

#### Answer:

(i) 15 kg 850 g in kilograms:

15 kg + 850 gm = 15 kg + $\frac{850}{1000}$ kg [Since 1 kg = 1000 gm]

15 kg + 0.850 kg = 15.850 kg

(ii) 8 kg 96 g in kilograms:

8 kg + 96 gm = 8 kg + $\frac{96}{1000}$kg [Since 1 kg = 1000 gm]

8 kg + 0.096 kg = 8.096 kg

(iii) 540 g in kilograms:

540 gm = $\frac{540}{1000}$ kg = 0.540 kg [Since 1 kg = 1000 gm]

(iv) 8 g in kilograms:

8 gm = $\frac{8}{1000}$ kg = 0.008 kg [Since 1 kg = 1000 gm]

#### Page No 118:

#### Question 36:

Using decimals, express

(i) Rs 18 and 25 paise in rupees

(ii) Rs 9 and 8 paise in rupees

(iii) 32 paise in rupees

(iv) 5 paise in rupees

#### Answer:

(i) Rs 18 and 25 paise in rupees:

Rs 18 + 25 paise = Rs 18 + Rs $\frac{25}{100}$ [Since Re 1 = 100 paise]

Rs 18 + Rs 0.25 = Rs 18.25

(ii) Rs 9 and 8 paise in rupees:

Rs 9 + 8 paise = Rs 9 + Rs $\frac{8}{100}$ [Since Re 1 = 100 paise]

Rs 9 + Rs 0.08 = Rs 9.08

(iii) 32 paise in rupees:

32 paise = Rs $\frac{32}{100}$ = Rs 0.32 [Since Re 1 = 100 paise]

(iv) 5 paise in rupees:

5 paise = Rs $\frac{5}{100}$ = Rs 0.05 [Since Re 1 = 100 paise]

#### Page No 120:

#### Question 1:

*Add the following decimals:*

9.6, 14.8, 37 and 5.9

#### Answer:

9.6, 14.8, 37 and 5.9

Converting the decimals into like decimals:

9.6, 14.8, 37.0 and 5.9

Let us write the given numbers in the column form.

Now, adding:

9.6

14.8

37.0

__ 5.9__

__ 67.3__

Hence, the sum of the given numbers is 67.3.

#### Page No 120:

#### Question 2:

*Add the following decimals:*

23.7, 106.94, 68.9 and 29.5

#### Answer:

23.7, 106.94, 68.9 and 29.5

Converting the decimals into like decimals:

23.70, 106.94, 68.90 and 29.50

Let us write the given numbers in the column form.

Now, adding:

23.70

106.94

68.90

__29.50__

__229.04__

Hence, the sum of the given numbers is 229.04.

#### Page No 120:

#### Question 3:

*Add the following decimals:*

72.8, 7.68, 16.23 and 0.7

#### Answer:

72.8, 7.68, 16.23 and 0.7

Converting the decimals into like decimals:

72.80, 7.68, 16.23 and 0.70

Let us write the given numbers in the column form.

Now, adding:

72.80

7.68

16.23

__ 0.70__

__97.41__

Hence, the sum of the given numbers is 97.41.

#### Page No 120:

#### Question 4:

*Add the following decimals:*

18.6, 84.75, 8.345 and 9.7

#### Answer:

18.6, 84.75, 8.345 and 9.7

Converting the decimals into like decimals:

18.600, 84.750, 8.345 and 9.700

Let us write the given numbers in the column form.

Now, adding:

18.600

84.750

8.345

__ 9.700__

__121.395__

Hence, the sum of the given numbers is 121.395.

#### Page No 120:

#### Question 5:

*Add the following decimals:*

8.236, 16.064, 63.8 and 27.53

#### Answer:

8.236, 16.064, 63.8 and 27.53

Converting the decimals into like decimals:

8.236, 16.064, 63.800 and 27.530

Let us write the given numbers in the column form.

Now, adding:

8.236

16.064

63.800

__27.530 __

__115.630__

Hence, the sum of the given numbers is 115.630.

#### Page No 120:

#### Question 6:

*Add the following decimals:*

28.9, 19.64, 123.697 and 0.354

#### Answer:

28.9, 19.64, 123.697 and 0.354

Converting the decimals into like decimals:

28.900, 19.640, 123.697 and 0.354

Let us write the given numbers in the column form.

Now, adding:

28.900

19.640

123.697

__0.354 __

__172.591__

Hence, the sum of the given numbers is 172.591.

#### Page No 120:

#### Question 7:

*Add the following decimals:*

4.37, 9.638, 17.007 and 6.8

#### Answer:

4.37, 9.638, 17.007 and 6.8

Converting the decimals into like decimals:

4.370, 9.638, 17.007 and 6.800

Let us write the given numbers in the column form.

Now, adding:

4.370

9.683

17.007

__ 6.800 __

__37.815 __

Hence, the sum of the given numbers is 37.815.

#### Page No 120:

#### Question 8:

*Add the following decimals:*

14.5, 0.038, 118.573 and 6.84

#### Answer:

14.5, 0.038, 118.573 and 6.84

Converting the decimals into like decimals:

14.500, 0.038, 118.573 and 6.840

Let us write the given numbers in the column form.

Now, adding:

14.500

0.038

118.573

__ 6.840 __

__139.951 __

Hence, the sum of the given numbers is 139.951.

#### Page No 120:

#### Question 9:

During three days of a week, a rickshaw puller earns Rs 32.60, Rs 56.80 and Rs 72 respectively. What is his total earning during these days?

#### Answer:

Earning on the 1st day of the week = Rs 32.60

Earning on the 2nd day of the week = Rs 56.80

Earning on the 3rd day of the week =__ Rs 72.00__

Total earning = __ Rs 161.40__

#### Page No 120:

#### Question 10:

A man purchases an almirah for Rs 11025, gives Rs 172.50 as its cartage and spends Rs 64.80 on its repair. How much does the almirah cost him?

#### Answer:

Cost of the almirah = Rs 11025.00

Money spent on cartage = Rs 172.50

Money spent on repair = __Rs 64.800__

Total cost of the almirah = __ Rs 11262.3 __

#### Page No 120:

#### Question 11:

Ramesh covers 36 km 235 m by taxi, 4 km 85 m by rickshaw and 1 km 80 m on foot What is the total distance covered by him?

#### Answer:

Distance covered by the taxi = 36 km 235 m

Distance covered by the rickshaw = 4 km 085 m

Distance covered on foot = __ 1 km 080 __m

Total distance covered = __41 km 400 m__

#### Page No 120:

#### Question 12:

A bag contains 45 kg 80 g of sugar and the mass of the empty bag is 950 g. What is the mass of the bag containing this much of sugar?

#### Answer:

Weight of sugar in the bag = 45 kg 080 g

Weight of the empty bag = __ 0 kg 950 g__

Total weight of the bag = __46 kg 030 g__

#### Page No 120:

#### Question 13:

Ramu bought 2 m 70 cm cloth for his shirt and 2 m 60 cm cloth for his pyjamas. Find the total length of cloth bought by him.

#### Answer:

Length of cloth for his shirt = 2 m 70 cm

Length of cloth for his pyjamas = __2 m 60 cm__

Total length of cloth bought = __5 m 30 cm__

#### Page No 120:

#### Question 14:

Radhika bought 2 m 5 cm cloth for her salwar and 3 m 35 cm cloth for her shirt. Find the total length of cloth bought by her.

#### Answer:

Length of cloth for her salwar = 2 m 05 cm

Length of cloth for her shirt = __3 m 35 cm__

Total length of cloth bought = __5 m 40 cm__

#### Page No 122:

#### Question 1:

*Subtract:*

27.86 from 53.74

#### Answer:

Let us write the numbers in the column form with the larger one at the top.

Now, subtracting:

53.74

- __27.86__

__ 25.88__

$\therefore $ 53.74 - 27.86 = 25.88

#### Page No 122:

#### Question 2:

*Subtract:*

64.98 from 103.87

#### Answer:

Let us write the numbers in the column form with the larger one at the top.

Now, subtracting:

103.87

-__ 64.98__

__ 38.89__

$\therefore $ 103.87 - 64.98 = 38.89

#### Page No 122:

#### Question 3:

*Subtract:*

59.63 from 92.4

#### Answer:

Converting the given numbers into like decimals:

59.63 and 92.40

Let us write them in the column form with the larger number at the top.

Now, subtracting:

92.40

- __59.63__

__ 32.77__

$\therefore $ 53.74 - 27.86 = 32.77

#### Page No 122:

#### Question 4:

*Subtract:*

56.8 from 204

#### Answer:

Converting the given numbers into like decimals:

56.80 and 204.00

Let us write them in the column form with the larger number at the top.

Now, subtracting:

204.00

- __56.80__

__ 147.2__

$\therefore $ 204.00 - 56.80 = 147.2

#### Page No 122:

#### Question 5:

*Subtract:*

127.38 from 216.2

#### Answer:

Converting the given numbers into like decimals:

127.38 and 216.20

Let us write them in the column form with the larger number at the top.

Now, subtracting:

216.20

-__ 127.38__

__ 88.82__

$\therefore $ 216.20 - 127.38 = 88.82

#### Page No 122:

#### Question 6:

*Subtract:*

39.875 from 70.68

#### Answer:

Converting the given numbers into like decimals:

39.875 and 70.680

Let us write them in the column form with the larger number at the top.

Now, subtracting:

70.680

- __39.875__

__ 30.805__

$\therefore $ 70.680 - 39.875 = 30.805

#### Page No 122:

#### Question 7:

*Subtract:*

348.237 from 523.12

#### Answer:

Converting the given numbers into like decimals:

348.237 and 523.120

Let us write them in the column form with the larger number at the top.

Now, subtracting:

523.120

- __348.237__

__ 174.883__

$\therefore $ 523.120 - 348.237 = 174.883

#### Page No 122:

#### Question 8:

*Subtract:*

458.573 from 600

#### Answer:

Converting the given numbers into like decimals:

458.573 and 600.000

Let us write them in the column form with the larger number at the top.

Now, subtracting:

600.000

- __458.573__

__141.427__

$\therefore $ 600.000 - 458.573 =141.427

#### Page No 122:

#### Question 9:

*Subtract:*

149.456 from 206.321

#### Answer:

Let us write the numbers in the column form with the larger one at the top.

Now, subtracting:

206.321

- __149.456__

__56.865__

$\therefore $ 206.321 - 149.456 = 56.865

#### Page No 122:

#### Question 10:

*Subtract:*

0.612 from 3.4

#### Answer:

Converting the given numbers into like decimals:

3.400 and 0.612

Let us write them in the column form with the larger number at the top.

Now, subtracting:

3.400

- __0.612__

__2.788__

$\therefore $ 3.400 - 0.612 = 2.788

#### Page No 122:

#### Question 11:

*Simplify:*

37.6 + 72.85 − 58.678 − 6.09

#### Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:

37.60 58.678

__+ 72.85 __ __ + 6.090 __

__ 110.45 __ __ 64.768 __

110.450

$-$__ 64.768__

__ 45.682__

(37.60 + 72.85) $-$ (58.678 + 6.090)

= 110.450 $-$ 64.768

= 45.682

#### Page No 122:

#### Question 12:

*Simplify:*

75.3 − 104.645 + 178.96 − 47.9

#### Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:

178.96 104.645

__+ 75.30 __ __ + 47.900__

__ 254.26 __ __ 152.545__

(75.30 + 178.96) $-$ (104.645 + 47.900)

254.260 $-$ 152.545

101.715 254.260

$-$__ 152.545__

__ 101.715__

#### Page No 122:

#### Question 13:

*Simplify:*

213.4 − 56.84 − 11.87 − 16.087

#### Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:

56.840

11.870

__+16.087 __

__ 84.797 __

(213.400) $-$ (56.840 + 11.870 + 16.087)

213.400 $-$ 84.797

128.603 213.400

$-$__ 84.797__

__128.603__

#### Page No 122:

#### Question 14:

*Simplify:*

76.3 − 7.666 − 6.77

#### Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:

7.666

__+ 6.770 __

__ 14.436 __

(76.300) $-$ (7.666 + 6.770)

= 76.300 $-$ 14.436

= 61.864

76.300

-__14.436__

__61.864__

#### Page No 122:

#### Question 15:

What is to be added to 74.5 to get 91?

#### Answer:

In order to get the number that must be added to 74.5 to get 91, we must subtract 74.5 from 91.0.

91.0

$-$__ 74.5__

__ 16.5__

Thus, 16.5 is the required number.

#### Page No 122:

#### Question 16:

What is to be subtracted from 7.3 to get 0.862?

#### Answer:

In order to get the number that must be subtracted from 7.300 to get .0862, we have to subtract 0.862 from 7.300.

7.300

$-$__ 0.862__

__ 6.438 __

Thus, 6.438 is the required number.

#### Page No 122:

#### Question 17:

By how much should 23.754 be increased to get 50?

#### Answer:

In order to get the number by which 23.754 must be increased to get 50, we have to subtract 23.754 from 50.000.

50.000

__$-$23.754__

__ 26.246__

#### Page No 122:

#### Question 18:

By how much should 84.5 be decreased to get 27.84?

#### Answer:

In order to get the number by which 84.50 must be decreased to get 27.84, we have to subtract 27.84 from 84.50.

84.50

__$-$27.84__

__ 56.66__

#### Page No 122:

#### Question 19:

If the school bags of Neelam and Garima weigh 6 kg 80 g and 5 kg 265 g respectively, whose bag is heavier and by how much?

#### Answer:

Weight of Neelam's school bag = 6080 g {Converting into grams: 6 kg + 80 g = (6000 + 80) g = 6080 g}

Weight of Garima's school bag = __$-$5265 g __ {Converting into grams: 5 kg + 265 g = (5000 + 265)g = 5265 g}

Difference of the weights of bags = __ 815 g__

Thus, the weight of Neelam's school bag is more than that of Garima's school bag by 815 grams, i.e. by 0.815 kg.

#### Page No 122:

#### Question 20:

Kunal purchased a notebook for Rs 19.75, a pencil for Rs 3.85 and a pen for Rs 8.35 from a book shop. He gave a 50-rupee note to the shopkeeper. What amount did he get back?

#### Answer:

Cost of the notebook = Rs 19.75

Cost of the pencil = Rs 3.85

Cost of the pen = + Rs__ 8.35__

Total cost payable = R__s____ 31.95__

Total money paid = Rs 50.00

Total money spent = $-$__Rs 31.95__

Balance = __Rs 18.05__

Thus, Kunal got back Rs 18.05 from the shopkeeper.

#### Page No 122:

#### Question 21:

Sunita purchased 5 kg 75 g of fruits and 3 kg 465 g of vegetables, and put them in a bag. If this bag with these contents weighs 9 kg, find the weight of the empty bag.

#### Answer:

Weight of the fruits = 5 kg 075 g

Weight of the vegetables = + __3 kg 465 g__

Total weight of the contents of the bag = __8 kg 540 g__

Total weight of the bag with its contents = 9 kg 000 g

Total weight of the contents of the bag = $-$__ 8 kg 540 g__

Weight of the empty bag = __ 0 kg 460 g__

Thus, the weight of the empty bag is 460 grams.

#### Page No 123:

#### Question 22:

The distance between Reeta's house and her office is 14 km. She covers 10 km 65 m by scooter, 3 km 75 m by bus and the rest on foot. How much distance does she cover by walking?

#### Answer:

Converting into metres:

10 km 65 m = (10 + 0.065) m = 10.065 m

3 km 75 m = (3 + 0.075) m = 3.075 m

Distance covered by the scooter = 10.065 km

Distance covered by the bus = __+ 3.075 km __

Total distance covered by the bus and the scooter = __ 13.140 km __

Total distance between the house and the office = 14.000 km

Total distance covered by the bus and the scooter = __$-$13.140 km __

Distance covered on foot = __ 0.860 km__

$\therefore $ Distance covered by walking = 0.860 km = 860 metres

#### Page No 123:

#### Question 1:

*Mark (✓) against the correct answer in each of the following:*

$\frac{7}{10}=?$

(a) 7.1

(b) 1.7

(c) 0.7

(d) 0.07

#### Answer:

(c) 0.7

$\frac{7}{10}$ = 7 tenths = 0.7

#### Page No 123:

#### Question 2:

*Mark (✓) against the correct answer in each of the following:*

$\frac{5}{100}=?$

(a) 5.1

(b) 5.01

(c) 0.5

(d) 0.05

#### Answer:

(d) 0.05

$\frac{5}{100}$ = 5 hundredths = 0.05

#### Page No 123:

#### Question 3:

*Mark (✓) against the correct answer in each of the following:*

$\frac{9}{1000}=?$

(a) 0.0009

(b) 0.009

(c) 9.001

(d) none of these

#### Answer:

(b) 0.009

$\frac{9}{1000}$ = 9 thousandths = 0.009

#### Page No 123:

#### Question 4:

*Mark (✓) against the correct answer in each of the following:*

$\frac{16}{1000}=?$

(a) 0.016

(b) 0.16

(c) 0.0016

(d) 1.006

#### Answer:

(a) 0.016

$\frac{16}{1000}$ = 16 thousandths = 0.016

#### Page No 123:

#### Question 5:

*Mark (✓) against the correct answer in each of the following:*

$\frac{134}{1000}=?$

(a) 13.4

(b) 1.34

(c) 0.134

(d) 0.0134

#### Answer:

(c) 0.134

$\frac{134}{1000}$ = 134 thousandths = 0.134

#### Page No 123:

#### Question 6:

*Mark (✓) against the correct answer in each of the following:*

$2\frac{17}{100}=?$

(a) 2.17

(b) 2.017

(c) 0.217

(d) 21.7

#### Answer:

(a) 2.17

2$\frac{17}{100}$ = 2 + $\frac{17}{100}$ = 2 + 0.17 = 2.17

#### Page No 123:

#### Question 7:

*Mark (✓) against the correct answer in each of the following:*

$4\frac{3}{100}=?$

(a) 4.3

(b) 4.03

(c) 4.003

(d) 43.10

#### Answer:

(b) 4.03

4$\frac{3}{100}$ = 4 + $\frac{3}{100}$ = 4 + 0.03 = 4.03

#### Page No 123:

#### Question 8:

*Mark (✓) against the correct answer in each of the following:*

6.25 = ?

(a) $6\frac{1}{2}$

(b) $6\frac{1}{4}$

(c) $62\frac{1}{2}$

(d) none of these

#### Answer:

b)

6.25 = 6 + 0.25 = 6 + $\frac{25}{100}$ = 6 + $\frac{1}{4}$ = $6\frac{1}{4}$

#### Page No 123:

#### Question 9:

*Mark (✓) against the correct answer in each of the following:*

$\frac{6}{25}=?$

(a) 2.4

(b) 0.24

(c) 0.024

(d) none of these

#### Answer:

(b) 0.24

$\frac{6}{25}$ = 0.24

__ __

25) 60 (0.24

__$-$50__

100

$-$__ 100__

__ 0 __

#### Page No 123:

#### Question 10:

*Mark (✓) against the correct answer in each of the following:*

$4\frac{7}{8}=?$

(a) 4.78

(b) 4.87

(c) 4.875

(d) none of these

#### Answer:

(c) 4.875

$4\frac{7}{8}$ = 4 + $\frac{7}{8}$ = 4 + 0.875 = 4.875

#### Page No 123:

#### Question 11:

*Mark (✓) against the correct answer in each of the following:*

24.8 = ?

(a) $24\frac{4}{5}$

(b) $24\frac{2}{5}$

(c) $24\frac{1}{5}$

(d) none of these

#### Answer:

(a) $24\frac{4}{5}$

24.8 = 24 + 0.8 = 24 + $\frac{8}{10}$ = 24 + $\frac{4}{5}$ = $24\frac{4}{5}$

#### Page No 124:

#### Question 12:

*Mark (✓) against the correct answer in each of the following:*

$2\frac{1}{25}=?$

(a) 2.4

(b) 2.04

(c) 2.004

(d) none of these

#### Answer:

(b) 2.04

$2\frac{1}{25}$ = 2 + $\frac{1}{25}$ = 2 + 0.04 = 2.04

#### Page No 124:

#### Question 13:

*Mark (✓) against the correct answer in each of the following:*

$2+\frac{3}{10}+\frac{4}{100}$

(a) 2.304

(b) 2.403

(c) 2.34

(d) none of these

#### Answer:

(c) 2.34

2 + $\frac{3}{10}+\frac{4}{100}$ = 2 + 0.3 + 0.04 = 2.34

#### Page No 124:

#### Question 14:

*Mark (✓) against the correct answer in each of the following:*

$2+\frac{6}{100}=?$

(a) 2.006

(b) 2.06

(c) 2.6

(d) none of these

#### Answer:

(b) 2.06

2 + $\frac{6}{100}$ = 2 + 0.06 = 2.06

#### Page No 124:

#### Question 15:

*Mark (✓) against the correct answer in each of the following:*

$\frac{4}{100}+\frac{7}{10000}=?$

(a) 0.47

(b) 0.407

(c) 0.0407

(d) none of these

#### Answer:

(c) 0.0407

$\frac{4}{100}+\frac{7}{10000}$ = 0.04 + 0.0007 = 0.0407

#### Page No 124:

#### Question 16:

The correct expanded from of 2.06 is

(a) $\left(2\times 10\right)+\left(6\times \frac{1}{10}\right)$

(b) $\left(2\times 1\right)+\left(6\times \frac{1}{10}\right)$

(c) $\left(2\times 1\right)+\left(6\times \frac{1}{100}\right)$

(d) none of these

#### Answer:

(c) $(2\times 1)+(6\times \frac{1}{100})$

2.06 = 2 + $\frac{6}{100}$

#### Page No 124:

#### Question 17:

Amoung 2.6, 2.006, 2.66 and 2.08, the largest number is

(a) 2.006

(b) 2.08

(c) 2.6

(d) 2.66

#### Answer:

(d) 2.66

Converting the given decimals into like decimals:

2.600, 2.006, 2.660 and 2.080

Among the given decimals, 2.660 is the largest.

#### Page No 124:

#### Question 18:

Which of the following is the correct order?

(a) 2.2 < 2.02 < 2.002 < 2.222

(b) 2.002 < 2.02 < 2.2 < 2.222

(c) 2.02 < 2.22 < 2.002 < 2.222

(d) none of these

#### Answer:

(b) 2.002 < 2.02 < 2.2 < 2.222

Converting the given decimals into like decimals:

2.002, 2.020, 2.200, 2.222

$\therefore $ 2.002 < 2.02 < 2.2 < 2.222

#### Page No 124:

#### Question 19:

Which is larger: 2.1 or 2.055?

(a) 2.1

(b) 2.055

(c) cannot be compared

#### Answer:

(a) 2.1

If we convert the given decimals into like decimals, we get 2.100 and 2.055.

At tenths place, 1 is greater than 0. Thus, 2.100 is greater than 2.055.

#### Page No 124:

#### Question 20:

*Mark (✓) against the correct answer in each of the following:*

1 cm = ?

(a) 0.1 m

(b) 0.01 m

(c) 0.001 m

(d) none of these

#### Answer:

(b) 0.01 m

1 m = 100 cm

$\therefore $ 1 cm = $\frac{1}{100}$m = 0.01 m

#### Page No 124:

#### Question 21:

*Mark (✓) against the correct answer in each of the following:*

2 m 5 cm = ?

(a) 2.5 m

(b) 2.05 m

(c) 2.005 m

(d) 0.25 m

#### Answer:

(b) 2.05 m

2 m 5 cm = (2 + $\frac{5}{100}$) m = (2 + 0.05) m = 2.05 m

#### Page No 124:

#### Question 22:

*Mark (✓) against the correct answer in each of the following:*

2 kg 8 g = ?

(a) 2.8 kg

(b) 2.08 kg

(c) 2.008 kg

(d) none of these

#### Answer:

(c) 2.008 kg

1 kg = 1000 g

$\therefore $ 2 kg 8 g = 2 kg + $\frac{8}{1000}$ kg = (2 + 0.008) kg = 2.008 kg

#### Page No 124:

#### Question 23:

*Mark (✓) against the correct answer in each of the following:*

2 kg 56 g = ?

(a) 2.56 kg

(b) 2.056 kg

(c) 2.560 kg

(d) none of these

#### Answer:

(b) 2.056 kg

2 kg + 56 g = (2 + $\frac{56}{1000}$) kg = (2 + 0.056) kg = 2.056 kg

#### Page No 124:

#### Question 24:

*Mark (✓) against the correct answer in each of the following:*

2 km 35 m = ?

(a) 2.35 km

(b) 2.350 km

(c) 2.035 km

(d) none of these

#### Answer:

(c) 2.035 km

1 km = 1000 m

$\therefore $ 2 km 35 m = (2 + $\frac{35}{1000}$) km = (2 + 0.035) km = 2.035 km

#### Page No 124:

#### Question 25:

*Mark (✓) against the correct answer in each of the following:*

0.4 + 0.004 + 4.4 = ?

(a) 4.444

(b) 5.2

(c) 4.804

(d) 5.404

#### Answer:

(c) 4.804

0.4 + 0.004 + 4.4

Converting into like decimals and then adding:

4.400

0.004

__+ 0.400__

__ 4.804__

#### Page No 124:

#### Question 26:

*Mark (✓) against the correct answer in each of the following:*

3.5 + 4.05 − 6.005 = ?

(a) 1.545

(b) 1.095

(c) 1.6

(d) none of these

#### Answer:

(a) 1.545

Converting into like decimals:

3.500 + 4.050 − 6.005

3.500

__+ 4.050__

__ 7.550__

7.550

−__ 6.005__

__ 1.545__

#### Page No 124:

#### Question 27:

*Mark (✓) against the correct answer in each of the following:*

6.3 − 2.8 = ?

(a) 0.35

(b) 3.5

(c) 3.035

(d) none of these

#### Answer:

(b) 3.5

6.3

− __2.8__

__3.5__

#### Page No 124:

#### Question 28:

*Mark (✓) against the correct answer in each of the following:*

5.01 − 3.6 = ?

(a) 4.65

(b) 1.95

(c) 1.41

(d) none of these

#### Answer:

(c) 1.41

Converting into like decimals and then subtracting:

5.01

− __3.60__

__ 1.41__

#### Page No 125:

#### Question 29:

*Mark (✓) against the correct answer in each of the following:*

2 − 0.7 = ?

(a) 1.3

(b) 1.5

(c) 2.03

(d) none of these

#### Answer:

(a) 1.3

Converting into like decimals and then subtracting:

2.0

−__ 0.7 __

__ 1.3__

#### Page No 125:

#### Question 30:

*Mark (✓) against the correct answer in each of the following:*

1.1 − 0.3 = ?

(a) 0.8

(b) 0.08

(c) 8

(d) none of these

#### Answer:

(a) 0.8

Converting into like decimals and then subtracting:

1.1

−__ 0.3__

__ 0.8__

#### Page No 126:

#### Question 1:

Convert $4\frac{5}{8}$ into a decimal fraction.

#### Answer:

$4\frac{5}{8}$ = 4 + $\frac{5}{8}$ = 4 + 0.625 = 4.625

#### Page No 126:

#### Question 2:

Express 105 cm into metres using decimals.

#### Answer:

1 cm = $\frac{1}{100}$ m

$\therefore $ 105 cm = $\frac{105}{100}$ m = (1 + $\frac{5}{100}$) m = (1 + 0.05) m = 1.05 m

#### Page No 126:

#### Question 3:

Express 6 km 5 m as km using decimals.

#### Answer:

1 m = $\frac{1}{1000}$ km

$\therefore $ 5 m = $\frac{5}{1000}$ km = 0.005 km

6 km 5 m = (6 + 0.005) km = 6.005 km

#### Page No 126:

#### Question 4:

Express 8 m as kilometre using decimals.

#### Answer:

1 m = $\frac{1}{1000}$ km

$\therefore $8 m = $\frac{8}{1000}$ km = 0.008 km

#### Page No 126:

#### Question 5:

Add 26.4, 163.05, 8.75 and 5.6.

#### Answer:

Converting into like decimals and then adding:

26.40

163.05

8.75

+__ 5.60__

__ 203.80__

#### Page No 126:

#### Question 6:

Subtract 0.528 from 3.2.

#### Answer:

Converting into like decimals and then subtracting:

3.200

$-$ __0.528__

__ 2.672__

#### Page No 126:

#### Question 7:

What is to be added to 63.5 to get 71?

#### Answer:

We subtract 63.5 from 71 in order to find the number that is to be added to 63.5 to make it 71.

Converting into like decimals and then subtracting:

71.0

$-$__ 63.5__

__ 7.5__

#### Page No 126:

#### Question 8:

What is to be subtracted from 13 to get 5.4?

#### Answer:

We subtract 5.4 from 13 in order to find the number that is to be subtracted from 13 to get 5.4.

Converting into like decimals and then subtracting:

13.0

$-$__ 5.4__

__ 7.6____ __

Thus, we need to subtract 7.6 from 13 to get 5.4.

#### Page No 126:

#### Question 9:

Arrange the following decimals in descending order:

6.5, 6.05, 6.54, 6.4 and 6.45

#### Answer:

6.5, 6.05, 6.54, 6.4 and 6.45

Converting into like decimals:

6.50, 6.05, 6.54, 6.40 and 6.45

Clearly, 6.54 > 6.50 > 6.45 > 6.40 > 6.05

Hence, the given decimals can be arranged in the descending order in the following manner:

6.54, 6.50, 6.45, 6.40 and 6.05

#### Page No 126:

#### Question 10:

Convert each of the following into a fraction in simplest form:

(i) .4

(ii) .35

(c) 0.08

(iv) 0.075

#### Answer:

(i) 0.4 = $\frac{4}{10}=\frac{2}{5}$

(ii) 0.35 = $\frac{35}{100}=\frac{7}{20}$

(iii) 0.08 = $\frac{8}{100}=\frac{2}{25}$

(iv) 0.075 = $\frac{75}{1000}=\frac{3}{40}$

#### Page No 126:

#### Question 11:

*Mark (✓) against the correct answer in each of the following:*

$\frac{3}{25}=?$

(a) 1.2

(b) 0.12

(c) 0.012

(d) none of these

#### Answer:

(b) 0.12

$\frac{3}{25}$ = 0.12

__ __

25) 30 (0.12

$-$ __25__

50

$-$__ 50 __

__ 0 __

#### Page No 126:

#### Question 12:

*Mark (✓) against the correct answer in each of the following:*

$\frac{6}{1000}=?$

(a) 6.001

(b) 0.0006

(c) 0.006

(d) 0.06

#### Answer:

(c) 0.006

$\frac{6}{1000}$ = 6 thousandths = 0.006

#### Page No 126:

#### Question 13:

*Mark (✓) against the correct answer in each of the following:*

$2\frac{3}{100}=?$

(a) 2.003

(b) 2.03

(c) 2.3

(d) none of these

#### Answer:

(b) 2.03

$2\frac{3}{100}$ = 2 + $\frac{3}{100}$ = 2 + 0.03 = 2.03

#### Page No 126:

#### Question 14:

*Mark (✓) against the correct answer in each of the following:*

The place value of 3 in 16.534 is

(a) $\frac{3}{10}$

(b) $\frac{3}{100}$

(c) $\frac{3}{1000}$

(d) 3

#### Answer:

(b) $\frac{3}{100}$

In 16.534, place value of 3 = 3 hundredths = 0.03 = $\frac{3}{100}$

#### Page No 126:

#### Question 15:

*Mark (✓) against the correct answer in each of the following:*

$4\frac{7}{8}=?$

(a) 4.78

(b) 4.87

(c) 4.875

(d) none of these

#### Answer:

(c) 4.875

$4\frac{7}{8}$ = 4 + $\frac{7}{8}$ = 4 + 0.875 = 4.875

#### Page No 126:

#### Question 16:

*Mark (✓) against the correct answer in each of the following:*

5.01 − 3.6 = ?

(a) 4.65

(b) 1.95

(c) 1.41

(d) none of these

#### Answer:

(c) 1.41

Converting into like decimals:

5.01

− __ 3.60__

__ 1.41__

#### Page No 126:

#### Question 17:

*Mark (✓) against the correct answer in each of the following:*

3.5 + 4.05 − 6.005 = ?

(a) 1.545

(b) 1.095

(c) 1.6

(d) none of these

#### Answer:

(a) 1.545

(3.50 + 4.05) $-$ 6.005

7.550 $-$ 6.005

Converting into like decimals and then adding:

3.50

+__ 4.05__

__ 7.55__

Converting into like decimals and then subtracting:

7.550

$-$__ 6.005__

__ 1.545__

#### Page No 126:

#### Question 18:

*Mark (✓) against the correct answer in each of the following:*

$\frac{4}{100}+\frac{7}{10000}=?$

(a) 0.47

(b) 0.407

(c) 0.0407

(d) none of these

#### Answer:

(c) 0.0407

$\frac{4}{100}+\frac{7}{10000}$ = 0.04 + 0.0007

Converting into like decimals:

0.0400 + 0.0007 = 0.0407

#### Page No 126:

#### Question 19:

*Mark (✓) against the correct answer in each of the following:*

Among 2.6, 2.006, 2.66 and 2.08, the largest number is

(a) 2.006

(b) 2.08

(c) 2.6

(d) 2.66

#### Answer:

(d) 2.66

Converting all the given decimals into like decimals:

2.600, 2.006, 2.660 and 2.080

Among these given like decimals, 2.660 is the largest.

#### Page No 126:

#### Question 20:

*Fill in the blanks.*

(i) 1 m = ...... km

(ii) 10 ml = ...... 1

(iii) 16 kg 5 g = ...... kg

(iv) 2 m 8 cm = ...... m

(v) 3.02, 4.75, 1.63 are examples of ...... decimals.

#### Answer:

(i) 1 m = $\frac{1}{1000}$ km = 0.001 km

(ii) 10 mL = $\frac{1}{100}$ 1 = 0.01 L

(iii) 16 kg 5 g = (16 + 0.005) kg = __16.005__ kg

(iv) 2 m 8 cm = (2 + 0.08) m = __2.08__ m

(v) 3.02, 4.75, 1.63 are examples of __like__ decimals.

#### Page No 127:

#### Question 21:

*Write 'T' for true and 'F' for false for each of the statements given below:*

(i) 3.02 < 3.2.

(ii) 3 g = 0.003 kg.

(iii) $\frac{341}{1000}=3.410.$

(iv) 6.2 and 6.200 are equivalent decimals.

(v) 2.3, 3.41, 4.53, 5.61 are examples of like decimals.

#### Answer:

(i) True

This is because after converting them into like decimals, we get 3.20 > 3.02, which is true.

(ii) True

1 g = $\frac{1}{1000}$ kg

$\therefore $ 3 g = $\frac{3}{1000}$ = 0.003 kg

(iii) False

$\frac{341}{1000}$ = 0.341

This is because it is equal to 341 thousandths.

(iv) True

(v) False

In this case, every decimal should have 2 decimals in order to be like decimals. But, 2.3 has only 1 decimal.

View NCERT Solutions for all chapters of Class 6