Question

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

\[\frac{77}{210}\]

Answer 1

 The given number is \[\frac{77}{210}\] and HCF(77, 210) = 7.

∴ \[\frac{77}{210} = \frac{77 \div 7}{210 \div 7} = \frac{11}{30}\]

Here, 

\[\frac{11}{30}\] is in its simplest form.

Now, 

\[30 = 2 \times 3 \times 5\]  is not of the form

\[2^m \times 5^n\]

So, the given number has a non-terminating repeating decimal expansion.