Order 2.1, 9/4, 2.05, -2 from smallest to largest

Step by step

The question

Question: put 2.1, 9/4, 2.05, −2 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.

4 times 25 is 100.

So we multiply the top and the bottom by 25.

225 hundredths is 2.25.

So 9/4 is 2.25.

2 Same number of digits

Zeros at the end of a decimal do not change it: 2.1 is the same as 2.10.

So we give every number 2 digits after the point.

3 Compare

Now they all have 2 digits after the point.

So we can forget the point and compare them like whole numbers: 205 < 210 < 225.

Careful!

More digits does not mean bigger.

Compare 2.05 with 2.10.

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: −2, 2.05, 2.1, 9/4.

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: −2, 2.05, 2.1, 9/4.

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.