Answer:
[tex]0.888=\frac{111}{125}[/tex]
Step-by-step explanation:
case A)
we have
[tex]0.888[/tex] -----> is not a repeating decimal
Let
[tex]x=0.888[/tex]
Multiply x by [tex]1,000[/tex]
[tex]1,000x=888[/tex]
Solve for x
Divide by [tex]1,000[/tex] both sides
[tex]x=888/1,000[/tex]
Simplify
[tex]x=111/125[/tex]
case B)
we have
[tex]0.888...[/tex] -----> is a repeating decimal
Let
[tex]x=0.888...[/tex]
Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:
[tex]10x=8.888..[/tex]
Subtract [tex]x[/tex] from [tex]\\10x[/tex]
[tex]10x-x=8.888..-0.888..=8[/tex]
The repeating decimals should cancel out
[tex]\\9x=8[/tex]
solve for x
Divide by [tex]9[/tex] both sides
[tex]x=8/9[/tex]
