RD Sharma 2013 Solutions for Class 6 Math Chapter 7 Decimals are provided here with simple step-by-step explanations. These solutions for Decimals are extremely popular among class 6 students for Math Decimals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma 2013 Book of class 6 Math Chapter 7 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma 2013 Solutions. All RD Sharma 2013 Solutions for class 6 Math are prepared by experts and are 100% accurate.

#### Question 1:

Write each of the following as decimals:

(i) Five hundred twenty five and forty hundredths.
(ii) Twelve and thirty five thousandths.
(iii) Fifteen and seventeen thousandths.
(iv) Eighty eight and forty eight-hundredths.

(i) = 525.40
(ii)  = 12.035
(iii)  = 15.017
(iv)  = 88.48

#### Question 2:

Write each of the following as decimals:

(i) $137+\frac{5}{100}$
(ii) $20+9+\frac{4}{100}$

#### Answer:

(i) We have 1 hundred, 3 tens, 7 ones and 5 hundredths.
Therefore, the decimal is137.05.

(ii) We have 2 tens, 9 ones and 4 hundredths.
Therefore, the decimal is 29.04.

#### Question 3:

Write each of the following as decimals:

(i) $\frac{8}{100}$
(ii) $\frac{300}{1000}$
(iii) $\frac{18}{1000}$
(iv) $\frac{208}{100}$
(v) $\frac{888}{1000}$

#### Answer:

(i) We have 8 hundredths.
Therefore, the decimal is 0.08.

(ii) In its lowest form, the fraction is $\frac{3}{10}$.
We have 3 tenths.
Therefore, the decimal is 0.3.

(iii) We have eighteen thousandths.
Therefore, the decimal is 0.018.

(iv)
We have 2 and 8 hundredths.
Therefore, the decimal is 2.08.

(v)
We have 8 tenths, 8 hundredths and 8 thousandths.
Therefore, the decimal is 0.888.

#### Question 4:

Write each of the following as decimals:

(i) $12\frac{1}{4}$
(ii) $7\frac{1}{8}$
(iii) $5\frac{1}{20}$

(i)
=

(ii)

(iii)

#### Question 5:

Write each of the following decimals as fractions. Reduce the fractions to lowest form:

(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 1.20
(v) 17.38

#### Answer:

(i) 0.04
=0 + 0.04
= 0 + 4 hundredths
=
= $\frac{4}{100}$
= $\frac{1}{25}$

(ii) 2.34
= 2 + 0.34
= 2 + 34 hundredths
= 2 + $\frac{34}{100}$
=
=
= $\frac{234}{100}$
= $\frac{117}{50}$

(iii) 0.342
= 0 + 342 thousandths
= $\frac{342}{1000}$
= $\frac{171}{500}$

(iv) 1.20
= 1 + 0.20
= 1 + 20 hundredths
= 1 + $\frac{20}{100}$
=
= $\frac{120}{100}$
= $\frac{6}{5}$

(v) 17.38
= 17 + 0.38
= 17 + 38 hundredths
= 17 + $\frac{38}{100}$
=
=
= $\frac{1738}{100}$
= $\frac{869}{50}$

#### Question 6:

Write each of the following as decimals:

(i) $20+9+\frac{4}{10}+\frac{1}{100}$
(ii) $30+\frac{4}{10}+\frac{8}{100}+\frac{3}{1000}$
(iii) $137+\frac{5}{100}$
(iv) $\frac{7}{10}+\frac{6}{100}+\frac{4}{1000}$
(v) $23+\frac{2}{10}+\frac{6}{1000}$
(vi) $700+20+5\frac{9}{100}$

#### Answer:

(i) Here, we have 2 tens, 9 ones, 4 tenths and 1 hundredths.
Therefore, the decimal is 29.41.

(ii) Here, we have 3 tens, 4 tenths, 8 hundredths and 3 thousandths.
Therefore, the decimal is 30.483.

(iii) Here, we have 1 hundred, 3 tens, 7 ones and 5 hundredths.
Therefore, the decimal is 137.05.

(iv) Here, we have 7 tenths, 6 hundredths and 4 thousandths.
Therefore, the decimal is 0.764.

(v)  Here, we have 2 tens, 3 ones, 2 tenths and 6 thousandths.
Therefore, the decimal is 23.206.

(vi) Here, we have 7 hundreds, 2 tens , 5 ones and 9 hundredths.
Therefore, the decimal is 725.09.

#### Question 1:

Express the following fractions as decimals:

(i) $\frac{23}{10}$
(ii) $\frac{139}{100}$
(iii) $\frac{4375}{1000}$
(iv) $12\frac{1}{2}$
(v) $75\frac{1}{4}$
(vi) $25\frac{1}{8}$
(vii) $18\frac{3}{24}$
(viii) $39\frac{7}{35}$
(ix) $15\frac{1}{25}$
(x) $\frac{111}{250}$

(i)  = 2.3

(ii) = 1.39

(iii) = 4.375

(iv) = = = 12.5

(v)

(vi) =

(vii)

(viii)

(ix)

(x)

#### Question 2:

Express the following decimals as fractions in the lowest form:

(i) 0.5
(ii) 2.5
(iii) 0.60
(iv) 0.18
(v) 5.25
(vi) 7.125
(vii) 15.004
(viii) 20.375
(ix) 600.75
(x) 59.48

(i)
(ii)
(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)
(x)

#### Question 1:

Fill in the blanks by using > or < to complete the following:

(i) 25.35....8.47
(ii) 20.695...20.93
(iii) 0.39...0.72
(iv) 0.109...0.83
(v) 0.236...0.201
(vi) 0.93...0.99

#### Answer:

(i) 25.35 > 8.47
Here, the whole part 23 > 8.

(ii) 20.695 < 20.93
Here, the whole parts are equal. Hence, we should check the tenth parts. Now, 9 is greater than 6.
Therefore, 20 + 6/10 +9/100 +5/1000 < 20 + 9/10 + 3/100.

(iii) 0.39 < 0.72
Here, the whole parts are 0. Hence, we should check the tenth parts. Now, 3<7.
Therefore, 3/10 +9/100 < 7/10 + 2/100.

(iv) 0.109 < 0.83
Here, the whole parts are 0. Hence, we should check the tenth parts. Now, 1<8.
Therefore, 1/10 +9/1000 < 8/10 + 3/100.

(v) 0.236 > 0.201
Here, the whole parts are 0. Hence, we should check the tenth parts in the two numbers, which are again equal.
So, we should now check the hundredth digit, 3 > 0.
Therefore, 2/10 +3/100 +6/1000 > 2/10 +0/100 +1/1000.

(vi) 0.93 < 0.99
Here, the whole parts are 0. Hence, we should check the tenth parts, which are again equal.
So, we should now check the hundredth digit, 3< 9.
Therefore, 9/10 + 3/100 < 9/10+9/100.

#### Question 2:

Which is greater? Give reason for your answer?

(i) 1.008 or 1.800
(ii) 3.3 or 3.300
(iii) 5.64 or 5.603
(iv) 1.5 or 1.50
(v) 1.431 or 1.439
(vi) 0.5 or 0.05

#### Answer:

(i) 1.008 < 1.800
The whole parts are equal, and comparing the tenth parts, we have 0 < 8.
Therefore, 1+ 0/10 +8/1000 < 1+8/10.

(ii) 3.3 = 3.300
The whole parts and the tenth parts are both equal.

(iii) 5.64 > 5.603
The whole parts and the tenth parts are both equal. Comparing the hundredth parts, we have 4 > 0.
Therefore, 5+ 6/10 + 4/100 > 5 + 6/10 + 0/100 + 3/1000.

(iv) 1.5 = 1.50
The whole parts and the tenth parts are both equal.

(v) 1.431 < 1.439
The whole parts, the tenth parts and the hundredth parts are all equal. Comparing the thousandth parts, we have 1 < 9.
Therefore, 1+ 4/10 + 3/100 + 1/1000 < 1+4/10 + 3/100 + 9/1000.

(vi) 0.5  > 0.05
The whole parts are both 0. Comparing the tenth parts, we have 5 > 0.
Therefore, 5/10 > 0/10 +5/100.

#### Question 1:

Express as Rupee (Rs) using decimals:

(i) 15 paisa
(ii) 5 paisa
(iii) 350 paisa
(iv) 2 rupees 60 paisa

#### Answer:

(i) 15 paisa
We know that 100 paisa = Rs 1.
Therefore, 1 paisa = Rs 1/100.
15 paisa = 15/100 = Rs 0.15

(ii) 5 paisa
We know that 100 paisa = Rs 1.
Therefore, 1 paisa = Rs 1/100.
5 paisa = 5/100 = Rs 0.05

(iii) 350 paisa
We know that 100 paisa = Rs 1.
Therefore, 1 paisa = Rs 1/100.
350 paisa = 350/100 = Rs 3.50

(iv) 2 rupees 60 paisa
We know that 100 paisa = Rs 1.
Therefore, 1 paisa = Rs 1/100.
2 rupees and 60 paisa =
= Rs 2.60

#### Question 2:

Express as metres (m) using decimals:

(i) 15 cm
(ii) 8 cm
(iii) 135 cm
(iv) 3m 65 cm

#### Answer:

(i) 15 cm
We know that 100 cm= 1 m.
Therefore, 1 cm = 1/100 m.
15 cm = 15*1/100 m = 15/100 = 0.15m

(ii) 8 cm
We know that 100 cm= 1 m.
Therefore, 1 cm = 1/100 m.
8 cm = 8/100= 0.08m

(iii) 135 cm
We know that 100 cm= 1 m.
Therefore, 1 cm = 1/100 m.
135 cm = 135/100 = 1.35 m

(iv) 3 m 65 cm
We know that 100 cm= 1 m.
Therefore, 1 cm = 1/100 m.
3m 65 cm = 3 + 65/100
= 3.65 m

#### Question 3:

Express as centimetre (cm) using decimals:

(i) 5 mm
(ii) 60 mm
(iii) 175 mm
(iv) 4cm 5 mm

#### Answer:

(i) 5 mm
We know that 10 mm = 1 cm.
Therefore, 1 mm = 1/10 cm.
5 mm = 5/10= 0.5 cm

(ii) 60 mm
We know that 10 mm = 1 cm.
Therefore, 1 mm = 1/10 cm.
60 mm = 60/10 = 6 cm

(iii) 175 mm
We know that 10 mm = 1 cm.
Therefore, 1 mm = 1/10 cm.
175 mm = 175/10 = 17.5 cm

(iv) 4 cm 5 mm
We know that 10 mm = 1 cm.
Therefore, 1 mm = 1/10 cm.
4 cm 5 mm =
= 4.5 cm

#### Question 4:

Express as kilometre (km) using decimals:

(i) 5 m
(ii) 55 m
(iii) 555 m
(iv) 5555 m
(v) 15 km 35 m

#### Answer:

(i) 5 m
We know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 km = 0.001 km.
5 m = 5/1000 = 0.005 km

(ii) 55 m
We know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 km = 0.001 km.
55 m = 55/1000 = 0.055 km

(iii) 555 m
We know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 km = 0.001 km.
555 m = 555/1000 = 0.555 km

(iv) 5555 m
We know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 km = 0.001 km.
5555 m = 5555/1000 = 5.555 km

(v) 15 km 35 m
We know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 km = 0.001 km.
15 km 35 m =
=15.035 km

#### Question 5:

Express as kilogram (kg) using decimals:

(i) 8 g
(ii) 150 g
(iii) 2750 g
(iv) 5 kg 750 g
(v) 36 kg 50 g

#### Answer:

(i) 8 g
We know that 1000 g = 1 kg.
Therefore, 1 g = 1/1000= 0.001 kg.
8 g = 8/1000= 0.008 kg

(ii) 150 g
We know that 1000 g = 1 kg.
Therefore, 1 g = 1/1000= 0.001 kg.
150 g = 150/1000 = 0.150 kg

(iii) 2750 g
We know that 1000 g = 1 kg.
Therefore, 1 g = 1/1000= 0.001 kg.
2750 g = 2.750 kg

(iv) 5 kg 750 g
We know that 1000 g = 1 kg.
Therefore, 1 g = 1/1000= 0.001 kg.
5 kg 750 g =
=5.750 kg

(v) 36 kg 50 g
We know that 1000 g = 1 kg.
Therefore, 1 g = 1/1000= 0.001 kg.
36 kg 50 g =
= 36.050 kg

#### Question 6:

Express each of the following without using decimals:

(i) Rs 5.25
(ii) 8.354 kg
(iii) 3.5 cm
(iv) 3.05 km
(v) 7.54 m
(vi) 15.005 kg
(vii) 12.05 m
(viii) 0.2 cm

#### Answer:

(i) Rs 5.25
We know that 100 paisa = 1 rupee.
So, 1 paisa = 1/100 rupee.
Therefore, Rs 5.25 = 5 + 0.25
=
= Rs 5 and 25 paisa

(ii) 8.354 kg
We know that 1000 g = 1 kg.
So, 1 g = 1/1000 kg.
Therefore, 8.354 = 8+ 0.354
=
= 8 kg 354 g

(iii) 3.5 cm
We know that 10 mm = 1 cm.
So, 1 mm = 1/10 cm.
Therefore, 3.5= 3+ 0.5
=
= 3 cm and 5 mm

(iv) 3.05 km
We know that 1000 m = 1 km.
Therefore, 3.05 = 3+ .05
= 3+ 5/100 = 3+ 50/1000 km
= 3 km and 50 m

(v) 7.54 m
We know that 100 cm = 1 m.
Therefore, 7.54 = 7+ 0.54
= 7+ 54/100
= 7 m and 54 cm

(vi) 15.005 kg
We know that 1 kg = 1000 g.
Therefore, 15.005= 15 + 0.005
= 15+ 5/1000
= 15 kg and 5 g

(vii) 12.05 m
We know that 1 m = 100 cm.
Therefore, 12.05 = 12 +.05
= 12 + 5/100
= 12 m and 5 cm

(viii) 0.2 cm
We know that 1 cm = 10 mm.
Therefore, 0.2 = 2/10
= 2 mm

#### Question 1:

Choose the decimal (s) from the brackets which is (are) not equivalent to the given decimals:

(i) 0.8                    (0.80, 0.85, 0.800, 0.08)
(ii) 25.1                 (25.01, 25.10, 25.100, 25.001)
(iii) 45.05              (45.050, 45.005, 45.500, 45.0500)

#### Answer:

(i) 0.85 and 0.08 are not equivalent to the given decimal.
In 0.85, we have 5 in the hundredth place, whereas in 0.8, we have nothing in the hundredth place.
In 0.08, 0 is in the tenth place, whereas in 0.8, 8 is in the tenth place.

(ii) 25.01 and 25.001 are not equivalent to the given decimal.
In 25.01, 0 is in the tenth place, whereas in 25.1, 1 is in the tenth place.
In 25.001, 0 is in the tenth place, whereas in 25.1, 1 is in the tenth place.

(iii) 45.005 and 45.500 are not equivalent to the given decimal.
In 45.005, 0 is in the hundredth place, whereas in 45.05, 5 is in the hundredth place.
In 45.500, 5 is in the tenth place, whereas in 45.05, 0 is in the tenth place.

#### Question 2:

Which of the following are like decimals:

(i) 0.34, 0.07, 5.35, 24.70
(ii) 45.05, 4.505, 20.55, 20.5
(iii) 8.80. 17.08, 8.94, 0.27
(iv) 4.50, 16.80, 0.700, 7.08

#### Answer:

(i) Like decimals, since these have the same number of digits after the decimal  point.

(ii) Unlike decimals, since these have different number of digits after the decimal point.

(iii) Like decimals, since these have the same number of digits after the decimal point.

(iv) Unlike decimals, since these have different number of digits after the decimal point.

#### Question 3:

Which of the following statements are correct?

(i) 8.05 and 7.95 are like decimals.
(ii) 0.95, 0.306, 7.10 are unlike decimals.
(iii) 3.70 and 3.7 are like decimals.
(iv) 13.59, 1.359, 135.9 are like decimals.
(v) 5.60, 3.04, 0.45 are like decimals.

#### Answer:

(i) Correct, since these two decimals have the same number of digits after the decimal point, only 2.

(ii) Correct, since these three decimals have different numbers of digits after the decimal point.

(iii) Incorrect, since these two decimals have different numbers of digits after the decimal point.

(iv) Incorrect, since these three decimals have different numbers of digits after the decimal point.

(v) Correct, since these three decimals have the same number of digits after the decimal point.

#### Question 4:

Convert each of the following sets of unlike decimals to like decimal:

(i) 7.8, 7.85
(ii) 2.02, 3.2
(iii) 0.6, 5.8, 12.765
(iv) 5.296, 5.2, 5.29
(v) 4.3294, 43.29, 432.94

#### Answer:

(i) Of the two given decimals, 7.85 has more decimal places, i.e., two, so we change 7.8 so that it has two decimal places.
Therefore, the like decimals are 7.80 and 7.85.

(ii) Of the two given decimals, 2.02 has more decimal places, i.e., two, so we change 3.2 so that it has two decimal places.
Therefore, the like decimals are 2.02 and 3.20.

(iii) Of the three given decimals, 12.765 has the highest number of decimal places, i.e., three, so we change the other two decimals so that they also have three decimal places.
Therefore, the like decimals are 0.600, 5.800 and 12.765.

(iv) Of the three given decimals, 5.296 has the highest number of decimal places, i.e., three, so we change the other two decimals so that they also have three decimal places.
Therefore, the like decimals are 5.296, 5.200 and 5.290.

(v) Among the three given decimals, 4.3294 has the highest number of decimal places, i.e., four, so we change all the decimals so that they also have four decimal places.
Therefore, the like decimals are 4.3294, 43.2900 and 432.9400.

#### Question 1:

Find the sum in each of the following:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(i)  102.360
+       7.054
+       0.800
=   110. 214

(ii)    0.060
+     4.108
+   91.500
=    95.668

(iii)   312.800
+      290.020
+      128.457
=      731.277

(iv)   113.285
+         6.700
+         9.340
+       30.080
=     159.405

(v)      3.420
+    264.080
+       7.600
+     95.321
=   370.421

(vi)    18.0030
+       41.7000
+       10.9500
+         5.0570
=       75.7100

#### Question 2:

Add the following

(i) 41.8, 39.24, 5.01 and 62.6
(ii) 4.702, 4.2, 6.02 and 1.27
(iii) 18.03, 146.3, 0.829 and 5.324

#### Answer:

(i)    41.80
+     39.24
+       5.01
+     62.60
=   148.65

(ii)       4.702
+     4.200
+     6.020
+     1.270
=       16.192

(iii)    18.030
+     146.300
+         0.829
+         5.324
=     170.483

#### Question 3:

Find the sum in each of the following:

(i) 0.007 + 8.5 + 30.08
(ii) 280.69 + 25.2 + 38
(iii) 25.65 + 9.005 + 3.7
(iv) 27.076 + 0.55 + 0.004

(i)   0.007
+    8.500
+  30.080
=  38.587

(ii)  280.69
+      25.20
+      38.00
=    343.89

(iii)  25.650
+      9.005
+      3.700
=    38.355

(iv)    27.076
+        0.550
+        0.004
=      27.630

#### Question 4:

Radhika's mother gave her Rs 10.50 and her father gave her Rs 15.80, find the total amount given to Radhika by her parents.

#### Answer:

Radhika's mother gave her Rs 10.50.
Radhika's father gave her Rs 15.80.

Total amount given to Radhika =
10.50
+15.80
= Rs 26.30

#### Question 5:

Rahul bought 4 kg 90 g apples, 2 kg 60 g of grapes and 5 kg 300 g mangoes. Find the weight of the fruits he bought in all.

#### Answer:

Weight of apples = 4 kg 90 g = 4.090 kg
Weight of grapes = 2 kg 60 g = 2.060 kg
Weight of mangoes = 5 kg 300 g =5.300 kg

Therefore, total weight of fruits bought by Rahul =
4.090 kg
2.060 kg
+  5.300 kg
=  11.450 kg

Total weight of the fruits  = 11.450 kg

#### Question 6:

Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for skirt. Find the total cloth bought by her.

#### Answer:

Cloth for shirt = 3 m 20 cm = 3.20 m       (we know that 1 m = 100 cm )
Cloth for  skirt = 2 m 5 cm= 2.05 m

Total cloth bought by Nasreen =
3.20 m
+ 2.05 m
= 5.25 m

Total cloth bought  = 5.25 m

#### Question 7:

Sunita travels 15 km 268 m by bus, 7 km 7 m by car and 500 m by foot in order to reach her school. How far is her school from her residence?

#### Answer:

Travel by bus = 15 km 268 m= 15.268 km (we know that 1 km = 1000 m)
Travel by car = 7 km 7 m = 7.007 km
Travel on foot = 500 m = 0.500 km

Total distance travelled =
15.268 km
7.007 km
+ 0.500 km
= 22.775 km

Therefore, Sunita's school is 22.775 km from her residence.

Subtract:

(i)

(ii)

(iii)

(iv)

(i)   46.23
- 37.50
=  8.73

(ii)   128.40
-    53.05
=       75.35

(iii) 45.03
- 27.80
=17.23

(iv)   23.930
-        5.946
=      17.984

#### Question 2:

Find the value of:

(i) 9.756 − 6.28
(ii) 21.05 − 15.27
(iii) 18.5 − 6.79
(iv) 48.1 − 0.37
(v) 108.032 − 86.8
(vi) 91.001 − 72.9
(vii) 32.7 − 25.86
(viii) 100 − 26.32

(i)      9.756
−     6.280
=    3.476

(ii)    21.05
−     15.27
=     5.78

(iii)    18.50
−        6.79
=       11.71

(iv)    48.10
−        0.37
=       47.73

(v)     108.032
−   86.800
=    21.232

(vi)  91.001
−72.900
= 18.101

(vii)  32.70
−     25.86
=       6.84

(viii)  100.00
−      26.32
=        73.68

#### Question 3:

The sum of two numbers is 100. If one of them is 78.01, find the order.

#### Answer:

One number is 78.01.
Suppose the other number is x.
The sum of these numbers is 100.
Therefore, 78.01 + x= 100.
x= 100 - 78.01
= 21.99

The other number is 21.99.

#### Question 4:

Waheeda's school is at a distance of 5 km 350 m from her house. She travels 1 km 70 m on foot and the rest she travels by bus. How much distance does she travel by bus?

#### Answer:

Distance travelled on foot = 1 km 70 m = 1.070 km (we know that 1 km = 1000 m)
Suppose distance travelled by bus = x km

Total distance of school from residence = 5 km 350 m = 5.350 km

So, 1.070 + x = 5.350
x= 5.350 - 1.070
x= 4.280 km

Therefore, distance travelled by bus = 4.280 km

#### Question 5:

Raju bought a book for Rs 35.65. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?

#### Answer:

Price of the book = Rs 35.65
Amount given to the shopkeeper = Rs 50
Therefore, balance returned by the shopkeeper
= Rs 50 - Rs 35.65
= Rs 14.35

#### Question 6:

Ruby bought a watermelon weighing 5 kg 200 g. Out of this she gave 2 kg 750 g to her neighbour. What is the weight of the watermelon left with Ruby?

#### Answer:

Weight of the watermelon when bought = 5 kg 200 g = 5.200 kg (we know that 1 kg = 1000 g)
Weight of the watermelon given to the neighbour  = 2 kg 750 g= 2.750 kg

Therefore, weight of the watermelon left with Ruby = Weight of the watermelon when bought - weight of the watermelon given to the neighbour

= 5.200 kg - 2.750 kg
= 2.450 kg
So, weight of the watermelon left with Ruby = 2.450 kg

#### Question 7:

Victor drove 89.050 km on Saturday and 73.9 km on Sunday. How many kilometres more did he drive on Saturday?

#### Answer:

Distance travelled on Saturday = 89.050 km
Distance travelled on Sunday = 73.9 km

Subtracting the distance travelled on Sunday from the distance travelled on Saturday
89.050 km - 73.9 km
= 15.15 km

Therefore, Victor drove 15.15 km more on Saturday.

#### Question 8:

Raju bought a book For Rs 35.65. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?

#### Answer:

Price of the book = Rs 35.65
Amount given to the shopkeeper = Rs 50
Therefore, balance returned by the shopkeeper
= Rs 50 - Rs 35.65
= Rs 14.35

#### Question 9:

Gopal travelled 125.5 km by bus, 14.25 km by pony and the rest of distance of Kedarnath on foot. If he covered a total distance of 150 km, how much did he travel on foot?

#### Answer:

Distance travelled by bus = 125.5 km
Distance travelled on pony = 14.25 km
Suppose the distance travelled on foot = x

Total distance = 150 km = Distance travelled by bus + distance travelled on pony + distance travelled on foot
150 km = 125.5 km + 14.25 km + x
150 km = 139.75 km + x
x = 150 km - 139.75 km
x=  10.25 km

Therefore, distance travelled on foot = 10.25 km

#### Question 10:

Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth form this for making a curtain. How much cloth is left with her?

#### Answer:

Length of cloth originally = 20 m 5 cm = 20.05 m (we know that 1 m = 100 cm)
Length of cloth cut for curtain = 4 m 50 cm = 4.50 m

Therefore, length of cloth left with Tina = Length of cloth originally - length of cloth cut for curtain
20.05 - 4.50
= 15.55 m

Length of cloth left with Tina = 15.55 m

#### Question 11:

Vineeta bought a book for Rs 18.80, a pen for Rs 8.50 and some papers for Rs 5.05. She gave fifty rupee to the shopkeeper. How much balance did she get back?

#### Answer:

Price of the book = Rs 18.90
Price of the pen = Rs 8.50
Price of the paper = Rs 5.05
Total price of the three items = Rs 18.90 + Rs 8.50 + Rs 5.05
= Rs 32.45
Total amount given to the shopkeeper = Rs 50
Therefore, balance received from the shopkeeper
= Total amount given to the shopkeeper - total price of the three items
= Rs 50 - Rs 32.45
= Rs 17.55

#### Question 12:

Tanuj walked 8.62 km on Monday, 7.05 km on Tuesday and some distance on Wednesday. If he walked 21.01 km in three days, how much distance did he walk on Wednesday?

#### Answer:

Distance travelled on Monday = 8.62 km
Distance travelled on Tuesday = 7.05 km
Suppose the distance travelled on Wednesday = x km

Total distance travelled in three days  = Distance travelled on (Monday + Tuesday + Wednesday)
21.01 = 8.62 + 7.05 + x
21.01 = 15.67 + x
x = 21.01 - 15.67 = 5.34

Therefore, Tanuj walked 5.34 km on Wednesday.

#### Question 1:

$\frac{3}{10}$ is equal to

(a) 3.1
(b) 1.3
(c) 0.3
(d) 0.03

#### Answer:

(c) 0.3
3/10 is equal to 0.3. Since the denominator is 10, we have to mark the decimal such that 3 is in the tenth place.

#### Question 2:

$\frac{7}{100}$ is equal to

(a) 7.1
(b) 7.01
(c) 0.7
(d) 0.07

#### Answer:

(d) 0.07
7/100 is equal to 0.07. Since the denominator is 100, we have to mark the decimal such that 7 is in the hundredth place.

#### Question 3:

$\frac{4}{1000}$ is equal to

(a) 0.004
(b) 0.04
(c) 0.4
(d) 4.001

#### Answer:

(a) 0.004
Since the denominator is 1000, we have to mark the decimal such that 4 is in the thousandth place.

#### Question 4:

The value of $\frac{37}{10000}$ is

(a) 0.0370
(b) 0.0037
(c) 0.00037
(d) 0.000037

#### Answer:

(b) 0.0037
Since the denominator is 10000, we have to mark the decimal such that 3 is in the thousandth place and 7 is in the ten-thousandth place.

#### Question 5:

The place value of 5 in 0.04532 is

(a) 5

(b) $\frac{5}{100}$
(c) $\frac{5}{1000}$
(d) $\frac{5}{10000}$

#### Answer:

(c) $\frac{5}{1000}$
5 is in the thousandth place.

0.04532 = 4/100 + 5/1000 + 3/10000 + 2/100000

#### Question 6:

The value of $\frac{231}{1000}$ is

(a) 0.231
(b) 2.31
(c) 23.1
(d) 0.0231

#### Answer:

(a) 0.231

We have 2 tenths, 3 hundredths and 1 thousandth.
Therefore, the value of 231/1000 is 0.231.

#### Question 7:

The value of $3\frac{5}{1000}$ is

(a) 3.5
(b) 3.05
(c) 3.005
(d) 3.0005

(c) 3.005

#### Question 8:

The value of $\frac{3}{25}$ is
(a) 1.2
(b) 0.12
(c) 0.012
(d) None of these

(b) 0.12

#### Question 9:

The value of $2\frac{1}{25}$ is
(a) 2.4
(b) 2.25
(c) 2.04
(d) 2.40

(c) 2.04

#### Question 10:

$4\frac{7}{8}$ is equal to

(a) 4.78
(b) 4.87
(c) 4.875
(d) None of these

(c) 4.875

#### Question 11:

$2+\frac{3}{10}+\frac{5}{100}$ is equal to

(a) 2.305
(b) 2.3
(c) 2.35
(d) 0.235

#### Answer:

(c) 2.35
3/10 = 0.3 (since the denominator is 10, we need to mark the decimal such that 3 is in the tenth place)
5/100= 0.05 (since the denominator is 100, we need to mark the decimal such that 5 is in the hundredth place)

Therefore, 2 + 3/10 + 5/100 = 2+ 0.3 + 0.05
= 2.35

#### Question 12:

$\frac{3}{100}+\frac{5}{10000}$ is equal to

(a) 0.35
(b) 0.305
(c) 0.0305
(d) 0.3005

#### Answer:

(c) 0.0305

3/100 = 0.03 (here, we have the denominator 100, so we mark the decimal such that 3 is in the hundredth place)
5/10000 = 0.0005 (here, we have the denominator 10000, so we mark the decimal such that 5 is in the ten thousandth place)

Therefore, 3/100 + 5/10000 = 0.03 + 0.0005
= 0.0305

1 cm is equal is

(a) 0.1 m
(b) 0.01 m
(c) 0.10 m
(d) 0.001 m

#### Answer:

(b) 0.01 m

We know that 100 cm = 1 m.
Therefore, 1 cm = 1/100 m = 0.01 m.

1 m is equal to

(a) 0.1 km
(b) 0.01 km
(c) 0.001 km
(d) 0.0001 km

#### Answer:

(c) 0.001 km

We  know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 m = 0.001 km.

#### Question 15:

2 kg 5 gm is equal to

(a) 2.5 kg
(b) 2.05 kg
(c) 2.005 kg
(d) 2.6 kg

#### Answer:

(c) 2.005 kg

We know that 1000 g = 1 kg.
Therefore,    1 g = 1/1000 kg = 0.001 kg
5 g = 5/1000 kg = 0.005 kg
Therefore, 2 kg 5 gm
=2 kg + 0.005 kg
= 2.005 kg

#### Question 16:

15 litres and 15 ml is equal to

(a) 15.15 litres
(b) 15.150 litres
(c) 15.0015 litres
(d) 15.015 litres

#### Answer:

(d) 15.015 litres
We know that 1000 ml = 1 litre.
Therefore,    1 ml = 1/1000 = 0.001 litre
15 ml = 15/1000 = 0.015 litre
So, 15 litre and 15 ml
= 15 litre  + 0.015 litre
= 15.015 litres

#### Question 17:

Which of the following are like decimals?

(a) 5.5, 5.05, 5.005, 5.50
(b) 5.5, 0.55, 5.55, 5.555
(c) 5.5, 6.6, 7.7, 8.8
(d) 0.5, 0.56, 0.567, 0.5678

#### Answer:

(c) 5.5. 6.6, 7.7, 8.8 are like decimals, since the number of decimals is the same.

#### Question 18:

The value of 0.5 + 0.005 + 5.05 is

(a) 5.55
(b) 5.555
(c) 5.055
(d) 5.550

(b) 5.555

#### Question 19:

0.35 − 0.035 is equal to

(a) 0.3
(b) 0.349
(c) 0.315
(d) 0.353

(c) 0.315

0.350
− 0.035
=0.315

#### Question 20:

2.5 + 3.05 − 4.005 is equal to

(a) 1.545
(b) 1.455
(c) 1.554
(d) 0.545

#### Answer:

(a) 1.545
2.5 + 3.05 − 4.005
= 5.55 − 4.005
= 1.545

#### Question 21:

Which is greater among 2.3, 2.03, 2.33, 2.05?

(a) 2.3
(b) 2.03
(c) 2.33
(d) 2.05

#### Answer:

(c) 2.33

The whole parts of all the above numbers are equal. Comparing the tenth parts, we see that two of the decimals have a tenth part 0 and two have a tenth part 3. Leaving aside the decimals that have a tenth part 0, we have 2.3 and 2.33. Comparing them, we find that 2.33 is greater than 2.3, because, in 2.3, there is no hundredth part, but in 2.33, the hundredth part is 3.

#### Question 1:

Write the following decimals in the place value table:

(i) 52.5
(ii) 12.57
(iii) 15.05
(iv) 74.059
(v) 0.503

#### Answer:

thousands hundreds tens ones tenths hundredths thousand
(i)     5 2   5
(ii)     1 2 5 7
(iii)     1 5 0 5
(iv)     7 4 0 5 9
(v)         5 0 3

The given decimals can be written as above in the place-value table.

#### Question 2:

Write the decimals shown in the following place value table:

 S.no Thousands Hundreds Tens Ones Tenths Hundredths Thousandths (i) 3 0 7 1 2 (ii) 9 5 4 3 0 2 5 (iii) 1 2 5 0 3

#### Answer:

The decimals shown in the above place-value table can be written as follows.

(i)    307.12

(ii)   9543.025

(iii)  12.503

#### Question 3:

Write each of the following decimals in words:

(i) 175.04
(ii) 0.21
(iii) 9.004
(iv) 0.459

#### Answer:

(i) One hundred seventy-five and four hundredths

(ii) Zero and twenty-one hundredths

(iii) Nine and four thousandths

(iv) Zero and four hundred fifty-nine thousandths

#### Question 4:

Write each of the following as decimals:

(i) $65+\frac{2}{10}+\frac{7}{100}$
(ii) $45+\frac{9}{100}$
(iii) $88+\frac{5}{10}+\frac{2}{1000}$
(iv) $\frac{3}{10}+\frac{7}{1000}$

#### Answer:

1)  We have 6 tens, 5 ones, 2 tenths and 7 hundredths.

Therefore, the decimal number is 65.27.

2) We have 4 tens, 5 ones and 9 hundredths.

Therefore, the decimal number is 45.09.

3) We have 8 tens, 8 ones, 5 tenths and 2 thousandths.

Therefore, the decimal number is 88.502.

4)  We have 3 tenths and 7 thousandths.

Therefore, the decimal number is 0.307.

#### Question 5:

Write each of the following as decimals:

(i) Five and four tenths
(ii) Twelve and four hundredths
(iii) Nine and Seven hundred five thousandths
(iv) Zero point five two six
(v) Forty seven and six thousandths
(vi) Eight thousandths
(vii) Nineteen and nineteen hundredths.

#### Answer:

(i) 5 + $\frac{4}{10}$ = 5.4

(ii) 12 + $\frac{4}{100}$ = 12.04

(iii) 9 + $\frac{705}{1000}$ = 9.705

(iv) 0.526

(v) 47 + $\frac{6}{1000}$= 47.006

(vi) $\frac{8}{1000}$ =  0.008

(vii) 19 + $\frac{19}{100}$ = 19.19

#### Question 1:

Write each of the following as decimals:

(i) Three tenths
(ii) Two ones and five tenths
(iii) Thirty and one tenths
(iv) Twenty two and six tenths
(v) One hundred, two ones and three tenths

#### Answer:

(i) $\frac{3}{10}$ = 0.3
(ii) 2 + $\frac{5}{10}$ = 2.5
(iii) 30 + $\frac{1}{10}$ = 30.1
(iv) 22 + $\frac{6}{10}$ = 22.6
(v) 100 + 2 + $\frac{3}{10}$ = 102.3

#### Question 2:

Write each of the following as decimals:

(i) $30+6+\frac{2}{10}$
(ii) $700+5+\frac{7}{10}$
(iii)
(iv) $200+70+9+\frac{5}{10}$

#### Answer:

(i) We have 3 tens, 6 ones and 2 tenths.

Therefore, the decimal is 36.2

(ii) We have 7 hundreds, 5 ones and 7 tenths.

Therefore, the decimal is 705.7.

(iii) We have 2 hundreds, 6 tens, 5 ones and 1 tenths.

Therefore, the decimal is 265.1.

(iv) We have 2 hundreds, 7 tens , 9 ones and 5 tenths.

Therefore, the decimal is 279.5.

#### Question 3:

Write each of the following as decimals:

(i) $\frac{22}{10}$
(ii) $\frac{3}{2}$
(iii) $\frac{2}{5}$

#### Answer:

(i) $\frac{22}{10}$
Since the denominator is ten, the decimal is 2.2.

(ii)  3/2
Making the denominator 10, we have
3/2

= $\frac{3×5}{2×5}$
= $\frac{15}{10}$
= 1.5

(iii)  2/5
Making the denominator 10, we have
2/5
= $\frac{2×2}{5×2}$
= $\frac{4}{10}$
= 0.4

#### Question 4:

Write each of the following as decimals:

(i) $40\frac{2}{5}$
(ii) $39\frac{2}{10}$
(iii) $4\frac{3}{5}$
(iv) $25\frac{1}{2}$

#### Answer:

(i)
To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get

= 40 + $\frac{2×2}{5×2}$
= 40 + $\frac{4}{10}$
= 40.4

(ii)
Here, the denominator is 10.
Therefore, the decimal is 39.2.

(iii)
To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get

= 4 + $\frac{3×2}{5×2}$
= 4 + $\frac{6}{10}$
=4.6

(iv)  $25\frac{1}{2}$ = 25 + $\frac{1}{2}$
To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get

=
=
=25.5

#### Question 5:

Write the following decimal as fractions. Reduce the fractions to lowest form:

(i) 3.8
(ii) 21.2
(iii) 6.4
(iv) 1.0

#### Answer:

(i) 3.8
= 3 + 8 tenths
= 3 + $\frac{8}{10}$
= $\frac{3×10}{10}$ + $\frac{8}{10}$ =

(ii)  21.2
= 21 + 2 tenths
= 21 + $\frac{2}{10}$ =

(iii) 6.4
= 6 + 4 tenths
= 6 + $\frac{4}{10}$
=

(iv)  1.0
Since the only number after the decimal is 0, the fraction is 1.

#### Question 6:

Represent the following decimal numbers on the number line:

(i) 0.2
(ii) 1.9
(iii) 1.1
(iv) 2.5

#### Answer:

(i) (ii) (iii) (iv) #### Question 7:

Between which two whole numbers on the number line are the given numbers? Which one is nearer the number?

(i) 0.8
(ii) 5.1
(iii) 2.6
(iv) 6.4
(v) 9.0
(vi) 4.9

#### Answer:

(i) 0.8 is between the two whole numbers 0 and 1.
As 0.8 is 8 units from 0 and 2 units from 1, it is nearer to 1.
(ii) 5.1 is between the two whole number 5 and 6.
As 5.1 is 1 unit from 5 and 9 units from 6, it is nearer to 5.
(iii) 2.6 is between 2 and 3.
As 2.6 is 6 units from 2 and 4 units from 3, it is nearer to 3.
(iv) 6.4 is between 6 and 7.
As 6.4 is 4 units from 6 and 6 units from 7, it is nearer to 6.
(v) 9.0 is itself a whole number, that is, 9.
(vi) 4.9 is between 4 and 5.
As 4.9 is 9 units from 4 and 1 unit from 5, it is nearer to 5.

#### Question 8:

Write the decimal number represented by the points on the given number line: A,B,C,D. #### Answer: A) 0.8, since A  is at the eighth place between 0 and 1

•
B) 1.3, since B is at the third place between 1 and 2

C) 1.9, since C is at the ninth place between 1 and 2

D) 2.6, since D is at the sixth place between 2 and 3

Disclaimer: The image given in the book is not consistent, as the number of periods between 0 and 1 is ten but the number of periods between 1 and 2 is seven. So, ignoring the position of the given numbers 1 , 2 and 3, it has been assumed that there are ten periods between every two consecutive numbers starting from the first point taken as zero.

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