How to Add or Subtract Decimals
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In mathematics, a decimal can be defined as a number which has two parts: a whole part and a fractional part, and these two parts are separated by a decimal point. The whole part always represents a number greater than one, while the fractional part, i.e., the part after the decimal, always represents a number less than one.
For example, let’s take the number 15.74. Now here the whole part is represented by 15, whereas the fractional part (74100 ) is represented by 74. Here 74 can also be denoted as the decimal part, as it lies after the decimal point.
Terminating and Non-Terminating Decimals
Terminating decimals are the one which have an end whereas non-terminating decimals don’t have an end. They are simply recurring digits that go on and on.
For example, 3.333333 , (103 ) is a recurring/non-terminating decimal, whereas 2.50 , (104 ) is a terminating decimal.
The Concept of Preceding Powers of 10
Now, there’s a very interesting concept linked to decimal numbers. This concept is known as the preceding powers of 10. All decimal numbers are based on this concept. So, as we move from left to right in a decimal number, basically, the place value of every digit gets divided by 10. So, the first digit after a decimal could be represented as 110 , second as 1100 and so on.
So, from this concept, we can easily find out the expanded form of a decimal.
For example, let’s take the decimal number 16.457. The expanded form could be written as: 10+6+410+5100+71000
Also, 16.457 can be represented as 164571000 in mixed fraction terms.
How to Add or Subtract 2 Decimals
To add or subtract 2 decimals, use the following steps:
- First, line up the two numbers as you would do in simple addition or subtraction.
- Next add zeroes to the right of decimals to match number of digits (if not same). For example, when performing (2.5−2.25), convert 2.5 to 2.50.
- Then perform simple column addition or subtraction.
Free printable Worksheets
Related Topics
How to Compare Decimals
How to Multiply and Divide Decimals
How to Convert Between Fractions, Decimals, and Mixed Numbers
How to Compare Decimals
Exercises for Adding and Subtracting Decimals
1) −114.33462.120
2) −129.74334.230
3) +121.37331.220
4) +114.64831.330
5) +129.49456.750
6) +136.97842.880
7) −136.71216.530
8) 123.428 + ___ =139.198
9) 130.666 + ___ =205.996
10) 123.389 + ___ =173.919
1) −114.33462.12052.214
First line up the numbers:−114.33462.120 , Start with the thousandth place 4−0=4, so −114.33462.1200.004 . Continue with hundredth place. 3−2=1 and then the tenth place 3−1=2 . −114.33462.1200.214 . Finally subtract the integer parts 114−62=52, −114.33462.12052.214.
2) −129.74334.23095.513
First line up the numbers:−129.74334.230 , Start with the thousandth place 3−0=3, so −129.22334.7300.003 . Continue with hundredth place. 4−3=1 and then the tenth place 7−2=5 . −114.33462.1200.513 . Finally subtract the integer parts 129−34=85, −129.74334.23095.513.
3) +121.37331.220152.593
First line up the numbers:+121.37331.220 , Start with the thousandth place 3+0=3, so +121.37331.2200.003 . Continue with hundredth place 7+2=9 and then the tenth place 3+2=5 . +121.37331.2200.593 . Finally subtract the integer parts 121+31=152, +121.37331.220152.593.
4) +114.64831.330145.978
First line up the numbers:+114.64831.330 , Start with the thousandth place 8+0=8, so +114.64831.3300.008 . Continue with hundredth place 4+3=7 and then the tenth place 6+3=9 . +114.64831.3300.978 . Finally subtract the integer parts 114+31=145, +114.64831.330145.978.
5) +129.49456.750186.244
6) +136.97842.880179.858
7) −136.71216.530120.182
8) 123.428 + ___ =139.198 ⇒139.198 − 123.428 = ___ ⇒−139.198123.42815.770
9) 130.666 + ___ =205.996 ⇒205.996 − 130.666 = ___ ⇒−205.996130.66675.330
10) 123.389 + ___ =173.919 ⇒173.919 − 123.389 = ___ ⇒−173.919123.38950.530
Adding and Subtracting Decimals Quiz