Question

7. Write down the decimal expansion of the following rational numbers by writing their
denominators in the form 2" x 5m, where n, m are non-negative integers.
[Basic/STANDARD]
1. 179/125
2. 251/5000


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Answer 1

Answer:

1. 179/125:

Denominator = 125 = 2^0 × 5^3

1. 251/5000

Denominator = 2^3 × 5^4

Explanation: The denominator can be written in form of 2^n × 5^m by prime factorisation.

N.B.:-

• min(n, m) is the number of decimal places after which it will terminate.

For example, in 251/5000, 5000 = 2^3 × 5^4. So, min(3, 4) = 3. So, after three decimal places, it will terminate.

• In case when denominator is not in form of 2^a × 5^b, the number is not terminating.
• In case when denominator is in form of 2^a × 5^b, the number will terminate.