# 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

Updated on: 10-Oct-2022

64 Views 