Without Actual Division, find which of the following rational numbers are terminating decimals

By K Balaji|Updated : November 13th, 2022

(i) 13/80

(ii) 7/24

(iii) 5/12

(iv) 31/375

(v) 16/125

Without actual division, the rational numbers 13/80 and 16/125 are terminating decimals.

A decimal that ends is known as a terminating decimal. It has a fixed number of digits and is a decimal.

Factors of the denominator for decimals that terminate should have the form of

2m x 5n

(i) 13/80

In the above digit the denominator is 80

80 = 2 × 2 × 2 × 2 × 5 = 24 × 5

Consequently, the denominator only has the factors 2 or 5.

As a result, the number is non-terminating.

(ii) 7/24

In the above digit the denominator is 24

24 = 2 × 2 × 2 × 3 = 23 × 3

Consequently, the denominator only has the factors 2 or 5.

As a result, the number is non-terminating.

(iii) 5/12

In the above digit the denominator is 12

12 = 2 × 2 × 3 = 22 × 3

Consequently, the denominator only has the factors 2 or 5.

As a result, the number is non-terminating.

(iv) 31/375

In the above digit the denominator is 375

375 = 5 × 5 × 5 × 3 = 53 × 3

Consequently, the denominator only has the factors 2 or 5.

As a result, the number is non-terminating.

(v) 16/125

In the above digit the denominator is 125

125 = 5 × 5 × 5 = 53

As a result, the denominator only has the factors 2 or 5.

As a result, the number is terminating.

Summary:-

Without Actual Division, find which of the following rational numbers are terminating decimals

The rational fractions 13/80 and 16/125 are terminating decimals without any actual division.

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