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

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Linear Equations in One Variable

Question

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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Given that

\frac{71}{75}

Here 71 and 75 have no common factors so 71 and 75 are co-prime

denominator = 75 = 5² = 3

∴ the denominator is not a form of

2 n .5 m

∴

\frac{71}{75}

is non terminating decimals