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

Rational Numbers

Question

Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals. $\frac{19}{45}$

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Given that

\frac{19}{45}

Here 19 and 45 have no common factors

so 19 and 45 are co prime

denominator = 45 = 9 × 5

∴ the denominator is of the form of

2 n .5 m

∴

\frac{19}{45}

is non terminating decimal