Question

How do you use long division to determine the decimal equivalent of 5/9?

Answer 1

`50 div5` gives an answer of `5` with a remainder of `5` each time.

`5/9 = 0.55555...... = 0.dot5`

Explanation:

The fraction `5/9` means `5 div 9` `color(white)(www)9 |bar(5.0000000......)`

`color(white)(wwwww)0.5color(white)(aaaaaaaa)larr 5div 9=0, 50div9=5`
`color(white)(www)9 |bar(5.0000000......)`
`color(white)(wwwww)ul4.5" "larr 0.5 xx 9`
`color(white)(wwwww)0.50" "larr` subtract, bring down a `0`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Same process again:

`color(white)(wwwww)0.55color(white)(aaaaaaaa)larr 50div9=5`
`color(white)(www)9 |bar(5.0000000......)`
`color(white)(wwwww)ul4.5`
`color(white)(wwwww)0.50`
`color(white)(ww.www)ul.45`
`color(white)(ww.www).050" "larr` subtract, bring down a `0`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Same process again and again:

`color(white)(wwwww)0.555555color(white)(aaaaaaaa)larr 50div9=5`
`color(white)(www)9 |bar(5.0000000......)`
`color(white)(wwwww)ul4.5`
`color(white)(wwwww)0.50`
`color(white)(ww.www)ul.45`
`color(white)(ww.www).050`
`color(white)(ww.www)ul.045`
`color(white)(ww.www).0050" "larr` subtract, bring down a `0`