Question

Find the decimal expansion of 7÷800 without actual division

Answer 1

Step-by-step explanation:

Given :-

7/800

To find :-

Find the decimal expansion of 7/800 ?

Solution :-

Given number = 7/800

It can be written as

=> 7/(2×2×2×2×2×5×5)

=> 7/(2^5×5^2)

On multiplying both numerator and the denominator with 5^3

=> (7×5^3)/(2^5×5^3×5^2)

=> (7×5^3)/(2^5×5^5)

=> (7×125)/(2×5)^5

=> 875/10^5

=> 875/100000

=>0.00875

Answer:-

The decimal expansion of 7/800 is 0.00875

Used formulae:-

• X = p/q is a rational number if the denominator q is in the form 2^m×5^n then X is the terminating decimal.

More points to know :-

• Every rational number can be expressed as either terminating decimal or non terminating recurring decimal.

• X = p/q is a rational number if the denominator q is not in the form 2^m×5^n then X is the non terminating decimal recurring decimal.