Question

How do you rewrite these in ascending order: `-8, -1, 2, 1.5, 2.6, 7, 2.32`?

Answer 1

`-8, -2,1.5,2, 2.32, 2.6,7`

Explanation:

Ascending order means we want the numbers to get increasingly bigger.

When doing something like this, let's think about the numbers in terms of temperature: a big negative number will be really cold and a big positive number will be really hot. We want to order the numbers from coldest to hottest.

Let's look at the negative numbers first. There are two of them:

`-8, -2`

`-8` is colder than `-2` so we'll order these:

`-8,-2,...`

Moving to the positive numbers, we have:

`2,1.5,2.6,7,2.32`

We can order these number first by looking at the ones position (the digit(s) to the left of the decimal point):

`1.5,2,2.6,2.32,7`

and so for sure the `1.5` is the smallest of the group and 7 the largest. So what about the numbers that have a 2 in the ones position:

`2, 2.6, 2.32`

To order these numbers, we move one digit to the right, to the tenths position. The `2` has an implied 0 and so is the smallest of the three numbers. `2.6` is bigger than `2.32` because 6 is bigger than 3. And so we order these three numbers as:

`2, 2.32, 2.6`

Add back in the 1.5 and the 7:

`1.5,2, 2.32, 2.6,7`

and lastly let's put back in the negative numbers:

`-8, -2,1.5,2, 2.32, 2.6,7`