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

Question

asked Feb 26, 2023 230k views

1 Answer

Chuckles · Answer 1 · 2023-03-03T18:29:51+0000

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

$1+0.888888888\ldots$

then equal the decimal part to x

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

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

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