Question

the decimal expansion of a rational number 11/2^3*5^2 Will terminate after how many places of decimals

Answer 1

Heya !!

$= \frac{11}{ {2}^{3} \times {5}^{2} } \\ \\ = \frac{11}{ {2}^{3} \times {5}^{2} } \times \frac{5}{5} \\ \\ = \frac{55}{ {2}^{3} \times {5}^{3} } \\ \\ = \frac{55}{ {10}^{3}} \\ \\ = 0.055$
Decimal point will terminate after three places.


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Answer 2

11/(2³  * 5²) will terminate after 3 places of decimal

Step-by-step explanation:

11/(2³  * 5²)

= 11/(2² * 2 * 5²)

= 11/( (2 * 5)²  * 2

= 11/(10² * 2)

= 11 * 5 /(10² * 2 * 5)

=  55 /(10² * 10)

= 55/10³

= 0.055

11/(2³  * 5²) will terminate after 3 places of decimal

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