Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$\frac{71}{75}$

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Solution

Given that $\frac{71}{75}$
Here $71$ and $75$ have no common factors so $71$ and $75$ are co-prime
denominator $= 75 = 5^{2} = 3$
$∴$ the denominator is not a form of $2^{n} . 5^{m}$
$∴$ $\frac{71}{75}$ is non terminating decimals

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Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.7175

Given that 7175Here 71 and 75 have no common factors so 71 and 75 are co-primedenominator =75=52=3∴ the denominator is not a form of 2n.5m∴ 7175 is non terminating decimals

Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$\frac{71}{75}$

Given that $\frac{71}{75}$
Here $71$ and $75$ have no common factors so $71$ and $75$ are co-prime
denominator $= 75 = 5^{2} = 3$
$∴$ the denominator is not a form of $2^{n} . 5^{m}$
$∴$ $\frac{71}{75}$ is non terminating decimals