Question

the decimal expansion of the rational number 359/2×5 to the power 4, will terminate after how many places of decimal ?​

Answer 1

Given:

$\frac{359}{(2*5)^{4}}$

To find:

The decimal expansion of the given number and terminates after how many places it terminates.

Solution:

The nature of the decimal expansion can be determined by the denominator.

If the denominator is 2 or 5 or 2 and 5, then the decimal expansion of the fraction will be terminating and if other than this then the decimal will be non-terminating or repeating.

We  have given the fraction as:

• $\frac{359}{(2*5)^{4}}$
• $\frac{359}{(10)^{4}}$

Here the power of the 10 is 4 so the decimal will four places before the one's place.

• $0.0359$

Means the decimal value of the given fraction will terminate after 4 places.

The decimal expansion of the given number is 0.0359 and terminates after 4 places.