Order -1 1/2, -1.4, 1/3, 0.3 from smallest to largest

Step by step

The question

Question: put −1 and 1/2, −1.4, 1/3, 0.3 in order, from smallest to largest.

1 Write each as a decimal

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

The minus is in front of the whole number.

1 and 1/2 means 1 plus 1/2.

2 times 5 is 10, so we multiply the top and the bottom by 5.

1/2 is 5 tenths: 0.5.

So −1 and 1/2 is −1.5.

Careful!

The 1 and the 2 are a fraction, not digits after the point.

1/2 is 0.5.

The bottom 3 does not go into 10, 100 or 1000.

So we divide: 1 divided by 3, one digit at a time.

10 divided by 3 is 3, with 1 left.

1 left again: the 3 repeats for ever.

So 1/3 is 0.333….

2 Same number of digits

Zeros at the end of a decimal do not change it: −1.5 is the same as −1.500.

A repeating decimal goes on for ever, so we can write as many of its digits as we need.

So we give every number 3 digits after the point.

3 Compare

Now both have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 300 < 333.

Negative numbers are below 0.

1500 > 1400, so −1.500 is further below 0.

Further below 0 means smaller.

Negative numbers are smaller than every positive number.

So they come first.

4 Write the answer

Now we write the numbers as they were given, in the same order: −1 and 1/2, −1.4, 0.3, 1/3.

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: −1 and 1/2, −1.4, 0.3, 1/3.

The same order.

So the answer is right!

Let's look back.

First: write each as a decimal.

Then: same number of digits.

Then: compare.

Then: write the answer.

Last: check.