15. A rational number can be expressed as terminating decimal when the factors of the
denominator are.........or.........only
Answers
Answered by
2
Answer:
15
Step-by-step explanation:
Any rational number with its denominator is in the form of 2
m
×5
n
, where m,n are positive integers and are terminating decimals. The examples are shown below:
(i)
8
15
=
2×2×2
15
=
2
3
15
=
2
3
×5
3
15×5
3
=
8×125
15×125
=
1000
1875
=1.875
(ii)
20
31
=
2×2×5
31
=
2×2×5×5
31×5
=
100
155
=1.55
In both the examples, the result is a terminating decimal because terminating decimal is a decimal which can be expressed in a finite number of figures.
Hence, a rational number can be expressed as a terminating decimal if the denominator has factors 2 or 5.
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