Question

what is decimal form of 17/125 without actual division?

Answer 1

Hello dear..

Answer:

Step-by-step explanation:

Any fraction where the denominator (the number under the line) can be written as a power of 2, a power of 5, or a multiple of such powers can be written as a terminating decimal. Why? Because 10=5*2. This means that 5^n * 2^m will divide without remainder into 10^n * 10^m = 10^(n+m). This means that it will terminate after not more than n+m places. It might run on a long way if n and m are big, but it will eventually terminate.

125 is equal to 5^3, so this is true of 125. It must divide into 10^3 = 1,000.

In fact, 125 is equal to (1/8) of 1,000, so you can multiply both the numerator and the denominator by 8 and you’re almost there.

7/125 = (7*8)/(125*8) = 56/1000

This can be written as 0.056.

Hope it helps..❤

Answer 2

Denominator = 125

= 5 x 5 x 5

Since, 5 is the only prime factor in the denominator.

the decimal form of the rational number 17/125 will be terminating type.