Without performing long division, determine which of the following rational numbers will have terminating decimals Class 9

Without performing long division, determine which of the following rational numbers will have terminating decimals Class 9

Question 1.

Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: $\frac{7}{20}, \frac{4}{15}$ and $\frac{13}{250}$

Then check your answers by explicitly performing the long divisions and expressing these rational numbers as decimals. Class 9

Solution:

i. $\frac{7}{20}$

20 = 2² × 5

Since the denominator has only prime factors 2 and 5.

∴ $\frac{7}{20}$ is a terminating decimal.

Verification:

∴ $\frac{7}{20}$ = 0.35

Hence, it is a terminating decimal.

ii. $\frac{4}{15}$

15 = 3 × 5

Since the denominator has a prime factor other than 2 and 5.

∴ $\frac{4}{15}$ is a non-terminating repeating decimal.

Verification:

Hence, it is a non-terminating repeating decimal.

iii. $\frac{13}{250}$

250 = 2 × 5³

Since the denominator has only prime factors 2 and 5.

∴ $\frac{13}{250}$ is a terminating decimal.

Verification:

∴ $\frac{13}{250}$ = 0.052

Hence, it is a terminating decimal.