A decimal number is of the form 3b 0276, wherebrepresents a digit The decimal is then written in the - Maths - Real Numbers

Question

A decimal number is of the form 3
b 0276, where
b represents a digit The decimal is
then written in the form of the simplest fraction The prime
factorisation of the denominator of the fraction is 2
2 × 5
4 × 7
x , where
x is a non-negative
integer

Ayushi Sharma · Accepted Answer

It is known that a rational
number p/q has a terminating decimal expansion, if
q can be prime factorised in the form
2n5m,
where n and m are non-negative
integers
Therefore, prime factorisation of the denominator of the
simplest fraction equivalent to the number 3b 0276 is
of the form
2n5m,
where n and m are non-negative
integers

It is given that prime
factorisation of the denominator of the simplest equivalent
fraction is 2^2 x 5^4 x 7^x
∴
2n5m
= 22 x
54 x
7x
⇒ 7x =
1
⇒ x = 0
Thus, the value of x is 0

A decimal number is of the form 3 b .0276, where b represents a digit. The decimal is then written in the form of the simplest fraction. The prime factorisation of the denominator of the fraction is 2 2 × 5 4 × 7 x , where x is a non-negative integer.

A decimal number is of the form 3 b .0276, where b represents a digit. The decimal is then written in the form of the simplest fraction. The prime factorisation of the denominator of the fraction is 2 ² × 5 ⁴ × 7 ^x , where x is a non-negative integer.