Question

Without dividing, determine whether the decimal form of fraction terminates or repeats. Explain. $\frac{5}{7}$

Answer 1

Checking whether the decimal form of fraction is terminating or repeating

The given fraction is $\frac{5}{7}$

$5$ and $7$ have no common factors and the given fraction is in simplest form.

We know that, if

• The prime factorisation of denominator of the fraction is of the form $2^m\times 5^n$, then the fraction is a terminating decimal.
• The prime factorisation of denominator of the fraction is of the form other than $2^m\times 5^n$ , then the fraction is a repeating decimal.

Here, the prime factorisation of $7$is not of the form $2^m\times 5^n$.

Hence, the given fraction is repeating decimal.