Check whether the following rational number has a terminating decimal expansion. If so, write down the decimal expansion.
$\frac{7}{80}$

 Given :

The given rational number is $\frac{7}{80}$.

To do :

We have to check the given rational number has a terminating decimal expansion

Solution :

The rational number $\frac{p}{q}$ is terminating, if,

i) p and q are coprime.

ii) q should be in the form of $2^n5^m$

In $\frac{7}{80}$,

7 and 80 has no common factors other than 1.

So, they are coprime.

$80 = 2 \times 2 \times 2 \times 2 \times 5 = 2^4 \times 5^1$

$\frac{7}{80}= \frac{7}{2^4 \times 5^1}$

So, denominator $2^4 \times 5^1$  is in the form of $2^n5^m$.

Therefore, the rational number $\frac{29}{343}$ has terminating decimal expansion.

 Decimal expansion of  $\frac{7}{80}$,

                         

                                 0.0875

                            _________________            

                     80 |    700

                           $-$ 640 

                           _________________

                                   600

                          $-$     560

                           __________________

                                      400

                                $-$  400

                          ___________________

                                        0

 

$\frac{7}{80} = 0.0875$

 

The decimal expansion of $\frac{7}{80}$ is 0.0875