Question

Write the following decimal number in its equivalent fraction form. Show all work for full credit. 0.888

Answer 1

0.888 = 888 / 1000

hope that helps

Answer 2

`0.888=(111)/(125)`

Explanation:

case A)

we have

`0.888` -----> is not a repeating decimal

Let

`x=0.888`

Multiply x by
`1,000`

`1,000x=888`

Solve for x

Divide by
`1,000` both sides

`x=888/1,000`

Simplify

`x=111/125`

case B)

we have

`0.888...` -----> is a repeating decimal

Let

`x=0.888...`

Multiply x by a power of
`10`, one that keeps the decimal part of the number the same:

`10x=8.888..`

Subtract
`x` from
`\\10x`

`10x-x=8.888..-0.888..=8`

The repeating decimals should cancel out

`\\9x=8`

solve for x

Divide by
`9` both sides

`x=8/9`