Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$\frac{26}{25}$

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Solution

Given that $\frac{26}{25}$
Here $25$ and $26$ have common factors
so $26, 25$ are co-prime
denominator $= 25$
$= 2^{0} . 5^{2}$
$∴$ the denominator is of the form of $2^{n} . 5^{n}$
$∴$ $\frac{26}{25}$ is a terminating decimal

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Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.2625

Given that 2625Here 25 and 26 have common factors so 26,25 are co-primedenominator =25=20.52∴ the denominator is of the form of 2n.5n∴ 2625 is a terminating decimal

Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$\frac{26}{25}$

Given that $\frac{26}{25}$
Here $25$ and $26$ have common factors
so $26, 25$ are co-prime
denominator $= 25$
$= 2^{0} . 5^{2}$
$∴$ the denominator is of the form of $2^{n} . 5^{n}$
$∴$ $\frac{26}{25}$ is a terminating decimal