Question

3.83 repeating as a fraction?

Answer 1

It depends upon how much of the given number you mean to be repeating.

Explanation:

`3.8bar3color(white)("xxxxx")`only the last digit `3` repeats:

`10x=color(white)("x")38.33333...`
`ul(-x)color(white)(=)ul(-color(white)(3)3.83333...`
`99x = color(white)("x")34.5`
`rarr x=(34.5)/90=23/60`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`3.bar(83)color(white)("xxxxxx")` the last 2 digits are repeating:

`100x=color(white)("x..")383.838383...`
`ul(-color(white)("..")x)=ul(-color(white)("xx")3.838383...)`
`color(white)(".")99x=color(white)("xx")380.0`
`rarr x=380/99`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`bar(3.83)color(white)("xxxxxx")`all 3 digits repeat:

`1000x =color(white)("..")3833.83383383...`
`ul(-color(white)("xx")x)=ul(-color(white)("....")3.83383383383...)`
`color(white)(".")999x=color(white)(".")3830.0`
`rarr x= 3830/999`