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

Jan 21, 2017

$- \pi , - 2.98 , - \sqrt{7} , - \frac{11}{5}$

#### Explanation:

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

$- \frac{11}{5} = - 2.2$

$- \pi = - 3.141$

$- 2.98 = - 2.98$

$- \sqrt{7} = - 2.646$

We can now order these from least to greates:

$- \pi , - 2.98 , - \sqrt{7} , - \frac{11}{5}$

Jan 31, 2017

$- \pi , \text{ "-2.98," "-11/5," } - \sqrt{7}$

#### 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.

$- \frac{11}{5} \text{ "-pi" "-2.98" } - \sqrt{7}$

Change format and use rounded values

$- {\left(2.5\right)}^{2} \text{ "-(3.1)^2" "-(2.98)^2" "-(sqrt7)^2" }$ which gives

$- 6.25 \text{ "-9. ....." "-8. ...... " } - 7$

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

$- \pi , \text{ "-2.98," "-11/5," } - \sqrt{7}$
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We do not need to know the exact values of $- {3.1}^{2} \mathmr{and} - {2.98}^{2}$

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