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.

\[\frac{35}{50}\]

Answer 1

The given number is \[\frac{35}{50}\]  and HCF(35, 50) = 5.

∴ \[\frac{35}{50} = \frac{35 \div 5}{50 \div 5} = \frac{7}{10}\]

Here,

\[\frac{7}{10}\]  is in its simplest form.

Now, 

\[10 = 2 \times 5\]  is of the form

\[2^m \times 5^n\] , where m = 1 and n = 1.

So, the given number has a terminating decimal expansion.