How do you order the rational numbers from least to greatest: 0.11, -1/9, -0.5, 1/10?

The easiest way to order rational numbers is to write them so that they are up to same places of decimal.

Here `-1/9=-0.11111111111111......`, where number `1` repeats endlessly, but other numbers do not last beyond hundredth place (i.e. second place after decimal point), hence we write numbers say upto five places only. Then

`0.11=0.11000`
`-1/9=-0.11111`
`-0.5=-0.50000`
`1/10=0.10000`

It is apparent that least number is one with negative sign but highest absolute (or numerical) value and among these it is `-0.50000` or `-0.5`, then comes `-0.11111=-1/9` and then we positive numbers of which `0.10000=1/10` is least and greatest is `0.11000=0.11`.

Hence, numbers from least to greatest are `{-0.5,-1/9,1/10,0.11}`

Note that the word 'least' is like saying 'less than'
There is a big difference between less than and smaller.

`-0.5 -=-1/2`

`-1/9 -> -1/9`

`0.11-=11/100`

`1/10-=10/100`

Now think of the position on the number line

`-1/9` is closer to 0 than is `-1/2." "` So `-1/2` is less than `-1/9`

`(1/10-=color(red)(10/100))` is less than `(0.11-=color(red)(11/100))`

So we have in order from left to right on the number line:

`-1/2"; "-1/9"; "10/100"; "11/100`

`-0.5"; "-1/9"; "1/10"; "0.11`