Question

Write 1.888... as a mixed number let ×=10×=10× - x = blank - blank 9× = x= So 1.888.. is equal to

Answer 1

First, we start to separate the whole part from the decimal part

`1+0.888888888\ldots`

then equal the decimal part to x

`x=0.8`

the number of digits that repeat itself is 1, so we multiply the equation by 10

`10x=8.8`

subtract both equations

`\begin{gathered} 10x-x=8.8-0.8 \\ 9x=8 \\ \\ x=\frac{8}{9_{}} \end{gathered}`

then we can write the decimal part as a fraction

`\bar{0.88}=(8)/(9)`

then 1.888 can be writen as a mixed number like

`1.8888\ldots=1(8)/(9)`