Order -0.25, -1/5, 0.1, -3/10 from smallest to largest Step by Step

Step by step

The question

Question: put −0.25, −1/5, 0.1, −3/10 in order, from smallest to largest.

−0.25, −15, 0.1, −310

1 Write each as a decimal

To compare, we write every number the same way: as a decimal.

A decimal is tenths, hundredths or thousandths.

5 times 2 is 10.

So we multiply the top and the bottom by 2.

2 tenths is 0.2.

The minus sign stays in front: −0.2.

= −15 = −1 × 25 × 2 = −210 = −0.2

3 tenths is 0.3.

The minus sign stays in front: −0.3.

= −310 = −0.3

2 Same number of digits

Zeros at the end of a decimal do not change it: −0.2 is the same as −0.20.

So we give every number 2 digits after the point.

= −0.25, −0.20, 0.10, −0.30

3 Compare

Negative numbers are below 0.

30 > 25 > 20, so the first one is further below 0.

Further below 0 means smaller.

= −0.30 < −0.25 < −0.20

30 > 25 > 20: further below 0

Careful!

0.3 is more than 0.25.

But −0.3 is further below 0, so it is smaller.

Careful: not −0.3 > −0.25 ✗

Negative numbers are smaller than every positive number.

So they come first.

= −0.30 < −0.25 < −0.20 < 0.10

4 Write the answer

Now we write the numbers as they were given, in the same order: −3/10, −0.25, −1/5, 0.1.

= −310 < −0.25 < −15 < 0.1

5 Check

Let's check on a number line.

Smaller numbers are further to the left.

We put a dot for each number.

From left to right: −3/10, −0.25, −1/5, 0.1.

The same order.

So the answer is right!

left to right: same order

Let's look back.

First: write each as a decimal.

Then: same number of digits.

Then: compare.

Then: write the answer.

Last: check.

Answer