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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Solution

Given that $\frac{19}{45}$
Here $19$ and $45$ have no common factors
so $19$ and $45$ are co prime
denominator $= 45 = 9 \times 5$
$∴$ the denominator is of the form of $2^{n} . 5^{m}$
$∴$ $\frac{19}{45}$ is non terminating decimal

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Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.1945

Given that 1945Here 19 and 45 have no common factorsso 19 and 45 are co primedenominator =45=9×5∴ the denominator is of the form of 2n.5m∴ 1945 is non terminating decimal

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

Given that $\frac{19}{45}$
Here $19$ and $45$ have no common factors
so $19$ and $45$ are co prime
denominator $= 45 = 9 \times 5$
$∴$ the denominator is of the form of $2^{n} . 5^{m}$
$∴$ $\frac{19}{45}$ is non terminating decimal