Question

How do you order the following from least to greatest `-11/5, -pi, -2.98, -sqrt7`?

Answer 1

`-pi, -2.98, -sqrt(7), -11/5`

Explanation:

First, let's convert each term into it's decimal equivalent:

`-11/5 = -2.2`

`-pi = -3.141`

`-2.98 = -2.98`

`-sqrt(7) = -2.646`

We can now order these from least to greates:

`-pi, -2.98, -sqrt(7), -11/5`

Answer 2

`-pi," "-2.98," "-11/5," "-sqrt7`

Explanation:

The numbers are all in different formats. A nifty way of doing this without a calculator is to square the numbers which will get rid of the square root.

`-11/5" "-pi" "-2.98" "-sqrt7`

Change format and use rounded values

`-(2.5)^2" "-(3.1)^2" "-(2.98)^2" "-(sqrt7)^2" "` which gives

`-6.25" "-9. ....." "-8. ...... " "-7`

From this it is possible to arrange the original numbers in ascending order.

`-pi," "-2.98," "-11/5," "-sqrt7`
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We do not need to know the exact values of `-3.1^2 and -2.98^2`

One is slightly less than -3 and the other slightly bigger.
Knowing this is enough to be able to rank them.