Question

Write the following decimal number in its equivalent fraction form. Show all work for full credit.

0.8(repeating)

Answer 1

Let x=0.8888...

x=0.8888 Start with the given equation

10x=8.8888 Multiply both sides by 10. The goal is to move the decimal point to the next repeating portion (which is just one spot to the right)



Now subtract the equation x=0.8888 from 10x=8.8888 to get
10x-x=8.8888-0.8888

9x=8 Combine like terms. Notice how the decimal portions cancel out.

x=8/9 Divide both sides by 9 to isolate x

So the answer is x=8/9 which means that 8/9=0.8888 (where the 8's repeat)