Working with decimals
Decimal values are parts of whole numbers, including tenths, hundredths and thousandths.
You can add and subtract decimal numbers in the same way as whole numbers using place value charts.
You can put the digits of each number into columns according to their place value, then subtract one from the other, starting with the smallest place value column.
Activity: Working to 3 decimal places
Complete this interactive activity to learn more about how to subtract decimals and then put your knowledge to the test with a quiz.
How to subtract decimals
A digit will have a different value depending on where it is positioned in a number. A place value chart can help show this.
When you subtract with decimals you must look carefully at the place value of each digit.
You subtract thousandths from the thousandths column, hundredths from the hundredths column and tenths from the tenths column.
If you need to exchange in order to be able to complete the subtraction, you do this in the same way as you do if you are working with whole numbers.
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Example 1
Which place value should you start with, when working out 4.178 - 0.042?
✓ You should start with the thousandths.
Follow these steps to work out the answer:
- Start with the thousandths. take 2 thousandths from 8 thousandths.
- Then look at the hundredths. Then subtract 4 hundredths from 7 hundredths.
- There are no tenths to subtract, so you can work out that the answer is 4.136
Example 2
You only have 4 tenths but need to subtract 5 tenths, what can you do?
✓ Just like working with whole numbers, you need to exchange.
You can take a whole 1, exchange it for 10 tenths, then move that to the tenths column.
Now you are taking 5 tenths away from 14 tenths, which leaves 9 tenths.
Finally subtract the 2 ones from the remaining 3 ones. This gives us the answer 1.932
Example 3
How can you check if 7.355 + 0.301 = 7.656 using subtraction?
✓ You can start with 7.656 and subtract 0.301.
In this calculation you need to subtract 3 tenths from the tenths column.
There are zero hundredths to be subtracted, but you need to subtract 1 thousandths from the thousandths column.
The answer is 7.355.
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More on Adding and subtracting
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