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LESSON: Ordering Decimals

READ: Compare Decimals

Compare Decimals

How can we compare decimals? When we compare decimals, we are trying to figure out which part of a whole is greater. To do this, we need to think about the number one.

1 is a whole. All decimals are part of one. The closer a decimal is to one, the larger the decimal is. How can we figure out how close a decimal is to one? This is a bit tricky, but if we look at the numbers and use place value we can figure it out.

Example

.45 ______ .67

Here we have two decimals that both have the same number of digits in them. When we compare our decimals need to have the same number of digits in them. Now we can look at the numbers without the decimal point. Is 45 or 67 greater?

67 is greater. We can say that sixty-seven hundredths is closer to one that forty-five hundredths.

Our answer is .45 < .67.


Steps for Comparing Decimals

  1. Be sure that the decimals you are comparing have the same number of digits in them.
  2. Think about the value of the number without the decimal point.
  3. The larger the number, the closer it is to one.


What do we do if the decimals we are comparing don’t have the same number of digits?

Example

.567 ______ .64

Five hundred and sixty-seven thousandths seems greater. After all it is thousandths after all the tricky part is that thousandths are smaller than hundredths. Is this true? To test this statement let’s look at a hundreds grid and a thousands grid.

Now it is easier to compare. You can see that .64 is larger than .567.


How can we compare without using a grid? Sometimes, we don’t have a grid to look at, what then? We can add zeros to make sure that digit numbers are equal. Then we can compare.

Example

.567 ______ .640

That made comparing very simple. 640 is larger than 567.

Our answer is that .567 < .640.


What about a decimal and a whole number? Sometimes, a decimal will have a whole number with it. If the whole number is the same, we just use the decimal part to compare.

Example

3.4 ______ 3.56

First, we add in our zeros.

3.40 ______ 3.56

The whole number, 3 is the same, so we can look at the decimal. 40 is less than 56 so we can use our symbols to compare.

Our answer is 3.4 < 3.56.