Order 0, -0.05, 0.5, 1/40 from smallest to largest

Step by step

The question

Question: put 0, −0.05, 0.5, 1/40 in order, from smallest to largest.

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.

40 times 25 is 1000.

So we multiply the top and the bottom by 25.

25 thousandths is 0.025.

So 1/40 is 0.025.

2 Same number of digits

Zeros at the end of a decimal do not change it: 0 is the same as 0.000.

So we give every number 3 digits after the point.

3 Compare

Now they all have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 0 < 25 < 500.

Careful!

More digits does not mean bigger.

Compare 0.025 with 0.500.

Negative numbers are smaller than 0 and every positive number.

So they come first.

4 Write the answer

Now we write the numbers as they were given, in the same order: −0.05, 0, 1/40, 0.5.

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: −0.05, 0, 1/40, 0.5.

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.