Question

Question 1 (x)
Without actually performing the long division, state whether$\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Answer 1

$\frac{77}{210}$
Simplify it by dividing numerator and denominator by 7 to get $\frac{11}{30}$.
On factorising the denominator, we get;
$30=2\times 3\times 5$
The denominator is not in the form of $2^m\times 5^n$.
Hence, the decimal expansion of $\frac{77}{210}$ is non terminating.