Write the decimal expansions of the following numbers.

Write the decimal expansions of the following numbers which have terminating decimal expansions:

(i) 17/8
(ii) 13/3125
(iii) 7/80
(iv) 6/15
(v) 2²×7/5⁴
(vi) 237/1500

Solution:

(i) 17/8
Rational and Irrational Numbers Class 9 ICSE ML Aggarwal img 22
17/8 = 2.125
(ii) 13/3125

13/3125 = 0.00416
(iii) 7/80

7/80 = 0.0875
(iv) 6/15
Let us divide both numerator and denominator by 3, we get
6/15 = (6 ÷ 3) / (15 ÷ 3)
= 2/5
Since the denominator is 5,
It is terminating decimal.
Rational and Irrational Numbers Class 9 ICSE ML Aggarwal img 25
6/15 = 0.4
(v) (2²×7)/5⁴
We know that the denominator is 5⁴
It is a terminating decimal.
(2²×7)/5⁴ = (2 × 2 × 7) / (5 × 5 × 5 × 5)
= 28/625

28/625 = 0.0448
It is a terminating decimal.
(vi) 237/1500
Let us divide both numerator and denominator by 3, we get
237/1500 = (237 ÷ 3) / (1500 ÷ 3)
= 79/500
Since the denominator is 500,
Its factors are, 500 = 2 × 2 × 5 × 5 × 5
= 2² × 5³
It is terminating decimal.
Rational and Irrational Numbers Class 9 ICSE ML Aggarwal img 27
237/1500= 79/500 = 0.1518