Check whether the following rational number has a terminating decimal expansion. If so, write down the decimal expansion.
$\frac{29}{343}$

Given :

The given rational number is $\frac{29}{343}$.

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 $\frac{29}{343}$,

29 and $343$ has no common factors other than 1.

So, they are coprime.

$343 = 7 \times 7 \times 7 = 7^3$

$\frac{29}{343}= \frac{29}{7^3}$

So, denominator $7^3$  is not in the form of $2^n5^m$.

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

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Updated on: 10-Oct-2022

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