Question

How do you rearrange these numbers from least to greatest `\{ - 3,- \frac { 7} { 2} ,6,\frac { 1} { 3} ,\sqrt { 3} ,0,8,- 5,9,- 11\}`?

Answer 1

Let's start with positive numbers:
`{6, 1/3,\sqrt(3),8,9}`
Rearrange it:
`{1/3,\sqrt(3),6,8,9}`
Look at the rest:
`{-3,-7/2=-3.5,0,-5,-11}`

Remember that more negative numbers are "smaller" then less negative numbers: for example `-2> -15`

Rearrange it, starting with `-11`.
`{-11,-5,-7/2,-3,0}`

The result is:
`{-11,-5,-7/2,-3,0,1/3,\sqrt(3),6,8,9}`

Answer 2

`-11,""-5," "-7/2," "-3," " 0," "1/3," "sqrt3," "6," "8," "9}`

Explanation:

Negative numbers are always smaller than positive numbers, so start with those. The further a negative number is away from `0`, the smaller it is.

`-3," "-7/2," "6," "1/3," "sqrt3," "0," "8," "-5," "9," "-11`

Negatives in order: `color(red)(-11," "-5," "-7/2," "-3)" "( -7/2 = -3.5)`

Compare the positives by changing them to decimals.

`sqrt 3 = 1.73 and 1/3 = 1.333`

positives in order:

`color(blue)(1/3," "sqrt3," "6," "8," "9)`

`0` is in the middle.

`{color(red)(-11,""-5," "-7/2," "-3," ") 0,""color(blue)(1/3,""sqrt3," "6," "8," "9)}`