Without performing division, state whether the rational number 13 3125 will have a terminating decimal form or a non-terminating, repeating decimal form.

Given rational number is 13 3125 . A simplified fraction of the form p q has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5 . Now, 13 3125 = 13 5 5 , q = 3125 = 5 5 As the only prime factor of the denominator is 5 , the decimal expansion will be terminating. Hence, 13 3125 will have terminating decimal form.

Without performing division, state whether the rational number 13 3125 will have a terminating decimal form or a non-terminating, repeating decimal form.

Given rational number is 13 3125 . A simplified fraction of the form p q has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5 . Now, 13 3125 = 13 5 5 , q = 3125 = 5 5 As the only prime factor of the denominator is 5 , the decimal expansion will be terminating. Hence, 13 3125 will have terminating decimal form.

Without performing division, state whether the rational number 11 12 will have a terminating decimal form or a non-terminating, repeating decimal form.

Given rational number is 11 12 . A simplified fraction of the form p q has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5 . Now, 11 12 = 11 3 × 2 2 The denominator q = 12 = 3 × 2 2 contains a prime factor 3 and the decimal expansion will be non-terminating. Hence, 11 12 will have a non-terminating decimal form.

Without performing division, state whether the rational number 64 455 will have a terminating decimal form or a non-terminating, repeating decimal form.

Given rational number is 64 455 . A simplified fraction of the form p q has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5 . Now, 64 455 = 64 5 × 7 × 13 The denominator q = 5 × 7 × 13 contains prime factors 5 , 7 , 13 which are other than 2 and 5 . So, the decimal expansion will be non-terminating. Hence, 64 455 will have a non-terminating decimal form.

Without performing division, state whether the rational number 15 1600 will have a terminating decimal form or a non-terminating, repeating decimal form.

Given rational number is 15 1600 . A simplified fraction of the form p q has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5 . Now, 15 1600 = 15 16 × 100 = 15 2 4 × 2 2 × 5 2 = 15 2 6 × 5 2 The denominator q = 1600 = 2 6 × 5 2 contains only prime factors 2 and 5 . So, the decimal expansion will be a terminating. Hence, 15 1600 will have a terminating decimal form.

Without performing division, state whether the rational number 29 343 will have a terminating decimal form or non-terminating, repeating decimal.

Here we need to check without performing division, whether the rational number 29 343 will have a terminating decimal form or non-terminating, repeating decimal. Let x = p q be a rational number, such that the prime factorization of q is of the form 2 n 5 m , then x is a terminating decimal, otherwise x is a non-terminating repeating decimal where n and m are non-negative integers. Now prime factorizing the terms, we get 29 343 = 29 7 × 7 × 7 ⇒ 29 343 = 29 7 3 Here the prime factorization of denominator is not of the form 2 n 5 m , where n and m are non-negative integers, then 29 343 has a decimal expansion which is non-terminating repeating.

Without performing division, state whether the rational number 23 2 3 5 2 will have a terminating decimal form or non-terminating, repeating decimal.

Here we need to check without performing division, whether the rational number 23 2 3 5 2 will have a terminating decimal form or non-terminating, repeating decimal. Let x = p q be a rational number, such that the prime factorization of q is of the form 2 n 5 m , then x is a terminating decimal, otherwise x is a non-terminating repeating decimal where n and m are non-negative integers. Given that 23 2 3 5 2 Here the prime factorization of denominator is of the form 2 n 5 m , where n and m are non-negative integers, then 23 2 3 5 2 has a decimal expansion which is terminating.

Without performing division, state whether the rational number 129 2 2 5 7 7 5 will have a terminating decimal form or non-terminating, repeating decimal.

Here we need to check without performing division, whether the rational number 129 2 2 5 7 7 5 will have a terminating decimal form or non-terminating, repeating decimal. Let x = p q be a rational number, such that the prime factorization of q is of the form 2 n 5 m , then x is a terminating decimal, otherwise x is a non-terminating repeating decimal where n and m are non-negative integers. Given that 129 2 2 5 7 7 5 = 43 × 3 2 2 5 7 7 5 Here the prime factorization of denominator is not of the form 2 n 5 m , where n and m are non-negative integers, then 129 2 2 5 7 7 5 has a decimal expansion which is non-terminating, repeating.

Without performing division, state whether the rational number 9 15 will have a terminating decimal form or non-terminating, repeating decimal.

Here we need to check without performing division, whether the rational number 9 15 will have a terminating decimal form or non-terminating, repeating decimal. Let x = p q be a rational number, such that the prime factorization of q is of the form 2 n 5 m , then x is a terminating decimal, otherwise x is a non-terminating repeating decimal where n and m are non-negative integers. Now prime factorizing the terms, we get, 9 15 = 3 2 3 × 5 = 3 5 Here the prime factorization of denominator is of the form 2 n 5 m , where n and m are non-negative integers, then 9 15 has a decimal expansion which is terminating.

Without performing division, state whether the rational number 36 100 will have a terminating decimal form or non-terminating, repeating decimal.

Here we need to check without performing division, whether the rational number 36 100 will have a terminating decimal form or non-terminating, repeating decimal. Let x = p q be a rational number, such that the prime factorization of q is of the form 2 n 5 m , then x is a terminating decimal, otherwise x is a non-terminating repeating decimal where n and m are non-negative integers. Now prime factorizing the terms, we get, 36 100 = 2 2 × 3 2 2 2 × 5 2 Here the prime factorization of denominator is of the form 2 n 5 m , where n and m are non-negative integers, then 36 100 has a decimal expansion which is terminating.

E M B I B E

Mathematics Class 10>Chapter 1 - Real Numbers>EXERCISE - 1.3>Q 2

EASY

10th Andhra Pradesh Board

IMPORTANT

Earn 100

Without performing division, state whether the rational number $\frac{13}{3125}$ will have a terminating decimal form or a non-terminating, repeating decimal form.

Important Questions on Real Numbers

EASY

10th Andhra Pradesh Board

IMPORTANT

Mathematics Class 10>Chapter 1 - Real Numbers>EXERCISE - 1.3>Q 2

Without performing division, state whether the rational number $\frac{11}{12}$ will have a terminating decimal form or a non-terminating, repeating decimal form.

MEDIUM

10th Andhra Pradesh Board

IMPORTANT

Mathematics Class 10>Chapter 1 - Real Numbers>EXERCISE - 1.3>Q 2

Without performing division, state whether the rational number $\frac{64}{455}$ will have a terminating decimal form or a non-terminating, repeating decimal form.

MEDIUM

10th Andhra Pradesh Board

IMPORTANT

Mathematics Class 10>Chapter 1 - Real Numbers>EXERCISE - 1.3>Q 2

Without performing division, state whether the rational number $\frac{15}{1600}$ will have a terminating decimal form or a non-terminating, repeating decimal form.

EASY

10th Andhra Pradesh Board

IMPORTANT

Mathematics Class 10>Chapter 1 - Real Numbers>EXERCISE - 1.3>Q 2

Without performing division, state whether the rational number