Question

Fractions in simplest form that have denominators of 2, 4,8,16, and 32 produce terminating decimals. Fractions with denominators of 6,12,18,and 24 produce repeating decimals. What causes the difference? Explain.

Answer 1

Explanation:

`2=2^1 ~divides 10\\4=2^2~divides~100\\8=2^3 divides~1000\\16=2^4~divides~10,000\\32=2^5~divides~100,000`

6,12,18,24 has one factor 3

which always gives a fraction when it divides 10,100,1000,... etc

e.g 5÷6=0.8333...