Question

Write down the decimal expansions of 7/80 and 13/125 by writing their denominators in the form of 2^m×5^n,where m,n are non negative integers.

Answer 1

The denominator of 7/80 is 80.
80=2×2×2×5×5=2³×5²
Here, decimal expansion of 80 is in the form of 2^m and 5^n. (m=3 and n=2). Therefore its decimal expansion will be terminating.

The denominator of 13/ 125 is 125.
125=5×5×5=5³
Here, decimal expansion of 125 is in the form of 2^m and 5^n. (m=0 and n=3). Therefore its decimal expansion will be terminating.

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Answer 2

Answer:

Step-by-step explanation:

7/80

• let us keep the numerator as it is
• take the prime factorisation of 80

taking prime factor of 80

7/2×2×2×2×5

=7/2^4×5^1

since denominator is in the form of 2^m×5^n.

∴it is terminating