Without actual division, find which of the following rational numbers are terminating decimals. (i) 13/80 (ii) 7/24 (iii) 5/12 (iv)31/375 (v) 16/125

Paloma Owens

Paloma Owens

Answered question

2023-03-25

Without actual division, find which of the following rational numbers are terminating decimals. (i) 1380 (ii) 724 (iii) 512 (iv)31375 (v) 16125

Answer & Explanation

pistuiescvzeb

pistuiescvzeb

Beginner2023-03-26Added 10 answers

Factors of the denominator for terminating decimals should take the form of 2 m × 5 n .
(i) 13 80
Here, denominator is 80
80 = 2 × 2 × 2 × 2 × 5 = 24 × 5
hence denominator doesn't have any factor other than 2 or 5.
So, the number is terminating.
(ii) 7 24
Denominator is 24.
24 = 2 × 2 × 2 × 3 = 23 × 3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.
(iii) 5 12
Denominator is 12.
12 = 2 × 2 × 3 = 22 × 3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.
(iv) 31 375
Denominator is 375.
375 = 5 × 5 × 5 × 3 = 53 × 3
Hence, denominator has factor other than 2 or 5.
The number is therefore not terminating.
(v) 16 125
denominator is 125.
125 = 5 × 5 × 5 = 53
As a result, the denominator only has the factors 2 or 5.
So, the number is terminating.

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