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CBSE Class 10 Answered

The decimal expansion of the rational numbers fraction numerator 43 over denominator 2 to the power of 4 cross times 5 cubed end fraction and fraction numerator 27 over denominator 2 cubed cross times 5 to the power of 4 cross times 3 squared end fraction will terminate after how many places of decimals ?
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Asked by susrisangita792 | 08 Apr, 2023, 08:43: AM
answered-by-expert Expert Answer
When the denominator of a rational number is in the form 2n x 5m
The decimal expansion terminates after n places if n>m or after m places if m>n
So,  fraction numerator 43 over denominator 2 to the power of 4 cross times 5 cubed end fraction will terminate after 4 places of decimals since 4>3
As the denominator of next rational number is 23 x 54 x 32
It has factors other than 2 and 5 which is 3.
So, its decimal expansion will be non-terminating and repeating.
Answered by Renu Varma | 10 Apr, 2023, 10:10: AM

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