Without actual division, find whether the following rational numbers are terminating decimals or recurring decimals:
(i) 13/45
(ii) -5/56
(iii) 7/125
(iv) -23/80
(v) – 15/66
In case of terminating decimals, write their decimal expansions.
Solution:
(i) 13/45
We know that
The fraction whose denominator is the multiple of 2 or 5 or both is a terminating decimal
In 13/45
45 = 3 × 3 × 5
Hence, it is not a terminating decimal.
(ii) In -5/56
56 = 2 × 2 × 2 × 7
Hence, it is not a terminating decimal.
(iii) In 7/125
125 = 5 × 5 × 5
We know that
Hence, it is a terminating decimal.
(v) In – 15/66
66 = 2 × 3 × 11
Hence, it is not a terminating decimal.
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