BMCC: Math Tutorials: Decimals:
Subtraction of Decimals
Quick links to topics on this page:
Subtracting Decimals
Estimating the Difference of Decimals
If necessary, you may want to review the terms associated with subtraction prior to starting on this section.
Subtraction of decimals is similar to addition of decimals, in that the operation is performed like subtraction of whole numbers, but while also keeping track of the decimal point positions. To subtract two decimals, the decimals need to be aligned so that the decimal points are directly above/below one another. That way, numbers of equal place value are being subtracted from one another. As suggested in the section of addition of decimals, you may find it easier to perform the subtraction if the minuend and subtrahend have the same number of digits to the right of the decimal point. If one of the numbers has less digits to the right of the decimal point than does the other number, extra zeros can be added after the final digit of the shorter number to bring it to the same length.
Example: Subtract 14.154 - 8.096 .
The first thing to do is line up the decimals so that the decimal point of the minuend is directly over the decimal point of the subtrahend. The minuend is 14.154 and the subtrahend is 8.096 . Aligning the decimal points gives:
In this example, both the minuend and the subtrahend have three digits to the right of the decimal point, so no trailing zeros need to be added to either number to fill in blank places. The next step is to perform the subtraction exactly as if these were whole numbers-- you can pretend that the decimal point isn't there at this stage.
The final step is to place a decimal point in the difference, so that it is directly below the decimal points in the minuend and subtrahend, thus ensuring that it lies between the ones place and the tenths place. In this example, the decimal point should be placed between the 6 and the 0 :
Another example: Subtract 6.12 - 0.0719 .
First, the problem needs to be written so the decimal points of the minuend and subtrahend are aligned:
The minuend has two less digits to the right of the decimal point than does the subtrahend, so let's fill in the two blank places with zeros:
Now the subtraction is performed as if we are dealing with whole numbers:
And the final step is to place the decimal point in the difference, directly below the decimal points in the minuend and subtrahend:
And a third example: Subtract 3.048 - 1.238 .
Lining up the decimals in the minuend and subtrahend, the problem looks like this:
Both numbers have three digits to the right of the decimal point, so no extra zeros have to be added to fill in empty places. Performing the subtraction as if these were whole numbers gives:
Placing the decimal point in the difference so that it is directly under the decimal points in the minuend and subtrahend gives:
Now the only thing left is to decide whether to leave the trailing 0 on the difference, or to remove it and record the result as 1.81 . As mentioned previously, this depends on the context of the problem.
Making an estimate of the difference of two decimals is done the same way as outlined for estimating the sum of two or more decimals. First, both numbers are rounded to the same place. Then the subtraction is performed as outlined above on this page.
Example: Estimate 21.063 - 19.3278 to the nearest hundredth.
The hundredths place is the second place to the right of the decimal point. Rounding the minuend (21.063) to the nearest hundredth gives 21.06 , and rounding the subtrahend (19.3278) to the nearest hundredth gives 19.33 . Now both decimals have two digits to the right of the decimal point. Aligning the decimal points and then subtracting as if these were whole numbers gives:
and inserting the decimal point into the appropriate place in the difference gives:
You can verify for yourself as an exercise that performing the subtraction without estimating yields an exact difference of 1.7352 .
Another example: Estimate 372.5 - 98.441 to the nearest ten.
The tens place is the second place to the left of the decimal point. Rounding 372.5 to the nearest ten gives 370 , and rounding 98.441 to the nearest ten gives 100 . After rounding, the subtraction problem is now 370 - 100 -- by rounding to the nearest ten we have turned both the minuend and subtrahend into whole numbers, and we no longer need to include a decimal point, although each number could still be written with one if we desire. Performing the subtraction gives:
You can verify for yourself that if the subtraction is performed without estimating, the exact difference is 274.059 .
Next: Multiplication of Decimals
[Previous Page] -- [Next Page]
[Top of Page] -- [Tutorials Home Page]
[BMCC Home Page] -- [E-mail the Tutorial Coordinator]
