# How do you order the following from least to greatest without a calculator #-sqrt10, -10/3, -3, -2.95, -3 1/4, -3.5 times 10^0#?

##### 1 Answer

A very nice question! Lots of maths involved, but easy to do with the use of a clever technique, Thanks Tony B

#### Explanation:

The boring way of doing this would be to just use a calculator to work out each one. There is a lot of basic maths in this question, and it is possible without a calculator.

To start, notice that:

- they are all negative values! The smallest is therefore the one furthest to the left on the number line. The one that looks the biggest is actually the smallest.
- They are in different forms - make them the same if possible
- They all lie close to
#3#

They are now easy to arrange, except for

(The bigger the denominator, the smaller the fraction, and the numerators are all 1)

The biggest number is clearly

Change the others into improper fractions.

Instead of working with

Let's square them all, then we will be able to see where 10 fits in.

(This is now in the reverse order, because they are all positive)

We can see that the first 3 numbers are all bigger than 10, so 10 lies before 9.

The final order is

But they must be in their original form.