Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
$\frac{35}{50}$

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Solution

Let,
$\frac{35}{50} = \frac{7}{10}$
Cheking co-prime
$7$ and $10$ have no common factor
Therefore,
$7$ and $10$ are co-prime.
For denominator $= 10 = 2^{1} \times 5^{1}$
Therefore,
denominator is of the form $2^{n} 5^{m}$
Where $m = 1. n = 1$
Hence the $\frac{7}{10}$ and $\frac{35}{50}$ are the terminating decimal.

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Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:3550

Let,3550=710Cheking co-prime 7 and 10 have no common factor Therefore,7 and 10 are co-prime.For denominator =10=21×51Therefore,denominator is of the form 2n5m Where m=1.n=1Hence the 710 and 3550 are the terminating decimal.

Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
$\frac{35}{50}$