Question

Check whether

7/50

and

3/28

will have terminating decimal expansion or not​

Answer 1

Answer:

$\frac{7}{50} = terminating \: decimal \: expansion \\ \\ \frac{3}{28} = not\: terminating \:repeating \:decimal \: expansion$

Step-by-step explanation:

A rational number have terminating decimal expansion only if the denominator of that rational number is in the form of

${2}^{n} {5}^{m}$

otherwise that number is not terminating repeating decimal .

for the first number 7/50; do the prime factors of denominator and then check whether it is in the form shown above.

$50 = 2 \times 5 \times 5 \\ \\ = 2 \times {5}^{2}$

yes, the denominator is in that form so the number 7/50 has terminating decimal expansion .

for the first number 3/28; do the prime factors of denominator and then check whether it is in the form shown above.

$28 = 2 \times 2 \times 7 \\ \\ = {2}^{2} \times 7$

No,the denominator is not in that form so the number 3/28 does not have terminating decimal expansion .

Hope it helps you.