Addition and Subtraction of Decimals

Decimal Addition and Subtraction

To add or subtract decimals, simply line up the decimal points and add or subtract the numbers on either side of the points.

For example, to add 1.23 and 2.56, line up the points like this:

1.23

+ 2.56

_____

3.79

Then, add the numbers on either side of the points:

1.23
+ 2.56
_____

3.79

3.79

Place Value in Decimals

In decimal notation, the place value of a digit depends on its position in the number. The rightmost digit (the ones place) is worth 1, the next digit to the left (the tens place) is worth 10, and so on. For example, the number 23.45 has a value of 23.45 because the 4 in the 45 is in the ones place and is worth 4, the 3 in the 23 is in the tens place and is worth 3, and the 2 in the 12 is in the hundreds place and is worth 2.

Addition of Decimal Numbers

When we add two decimal numbers, the first thing we do is align the decimal points. This is done by shifting the numbers to the right so that the decimal points are directly above each other.

Then, we add the numbers as if they were whole numbers. We ignore the decimal points and carry the numbers over as necessary.

Finally, we add the decimal points together. This gives us the total sum of the decimal numbers.

Steps to Add Decimals

To add decimals, follow these steps:

1. Write the numbers you are adding next to each other, with a decimal point between them.

2. Add the numbers together, and put the decimal point in the answer.

3. If there are decimals in the numbers you are adding, keep track of how many decimal places the answer has. If the answer has more decimal places than the numbers you are adding, round the answer to the nearest whole number.

4. If the answer has fewer decimal places than the numbers you are adding, write the number of decimal places in the answer.

Addition of Decimals Examples

+0.5

+0.7

+1.1

+1.5

+2.2

Subtraction of decimals

To subtract two decimals, line the decimals up on the right, and subtract the numbers in the ones column. If the number in the ones column is 5 or more, subtract the number in the tens column. If the number in the ones column is less than 5, subtract 1 from the number in the tens column.

2.5 – 1.6

2.5 – 1.6 = 0.9

Steps to Subtract Decimals

To subtract decimals, follow these steps:

Line the decimals up on two lines so that the digits in the ones and tenths column are lined up. If there is a number in the hundredths column, line it up with the number in the tenths column. If there is a number in the thousandths column, line it up with the number in the hundredths column.

Subtract the numbers in the ones column.

Subtract the numbers in the tenths column.

Subtract the numbers in the hundredths column.

Subtract the numbers in the thousandths column.

Subtraction of Decimals Examples

Example 1

Subtract 0.012 from 0.015

0.015 – 0.012 = 0.003