Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$\frac{1}{12}$

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Solution

Given that $\frac{1}{12}$
Here $1$ and $12$ have no common factors and
$1$ and $12$ are co-prime

For denominator $12$
$= 2^{2} \times 3$
$∴$ the denominator is not of the form $2^{n} . 5^{m}$
Thus $\frac{1}{12}$ has a 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.112

Given that 112Here 1 and 12 have no common factors and 1 and12 are co-primeFor denominator 12=22×3∴ the denominator is not of the form 2n.5mThus 112 has a non terminating decimals.

Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$\frac{1}{12}$

Given that $\frac{1}{12}$
Here $1$ and $12$ have no common factors and
$1$ and $12$ are co-prime

For denominator $12$
$= 2^{2} \times 3$
$∴$ the denominator is not of the form $2^{n} . 5^{m}$
Thus $\frac{1}{12}$ has a non terminating decimals.