Adding decimals is very similar to adding whole numbers. Just follow the three rules below in the order they are listed here!
Rule #1: Make sure that the decimal numbers you are adding are like decimals. For example, 2.325 and 4.8 are not like decimals since they do not have the same number of decimal places or the same number of digits to the right of the decimal point.
Just add zeros as placeholders until the decimals are like decimals. For example, just add two zeros as placeholders after 8 to get 4.800. Now, 2.325 and 4.800 have the same number of decimal places.
Rule #2: Once the decimals are in vertical format, the most important rule, in my opinion, is to align the decimal points and keep the digits with the same place value in the same column. This will ensure that you do not add tenths to hundredths or hundredths to thousandths and so forth.
Rule #3: If you have done rule #1 and rule #2, you are ready to add digits that have the same place value. Remember to carry numbers when necessary just like you do when adding whole numbers.
Finally, do not forget to write the decimal point that is located between the digit in the ones place and the digit in the tenths place!
Don't line up the last digits on the right. For 2.325 + 4.8, putting the 8 under the 5 adds 8 tenths to 5 thousandths and gives the wrong answer 2.333. Line up the decimal points instead.
A whole number has a decimal point at its end, even if it isn't written: 5 = 5.0 = 5.00.
Make 6.7 and 3.452 like decimals.
6.700 and 3.452. 3.452 has 3 decimal places, so add two zeros after the 7 in 6.7.
| 1 | |||||
| 2 | . | 3 | 2 | 5 | |
| + | 4 | . | 8 | 0 | 0 |
| 7 | . | 1 | 2 | 5 |
2.325 + 4.8 = 7.125
Example 2: Add 12.47 + 3.9 + 0.68
Make like decimals: 3.9 becomes 3.90. Then line up the decimal points and add.
| 2 | 1 | ||||
| 1 | 2 | . | 4 | 7 | |
| 3 | . | 9 | 0 | ||
| + | 0 | . | 6 | 8 | |
| 1 | 7 | . | 0 | 5 |
Hundredths: 7 + 0 + 8 = 15. Write 5, carry 1 to the tenths.
Tenths: 1 (carried) + 4 + 9 + 6 = 20. Write 0, carry 2 to the ones.
Ones: 2 (carried) + 2 + 3 + 0 = 7. Write 7.
Tens: 1. Write 1.
12.47 + 3.9 + 0.68 = 17.05
Check the answer with an estimate. Round each number to the nearest whole number and add: 2.325 + 4.8 is about 2 + 5 = 7, and 7.125 is close to 7, so the decimal point is in the right place.
Add 3.6 + 1.75.
5.35. Write 3.6 as 3.60. Hundredths: 0 + 5 = 5. Tenths: 6 + 7 = 13, write 3 and carry 1. Ones: 1 + 3 + 1 = 5.
Problem 1 guides you through every step, from making like decimals to writing the decimal point. Problem 2 uses fewer, bigger steps, with a hint for each one. Problem 3 gives no help: you fill in the whole addition yourself. You can skip a problem at any time, and each time you play you get new problems.
Practice Complete!
Type 2 to 4 numbers, each with up to 6 digits before the decimal point and up to 4 digits after it, then make your grid. The grey zeros are the placeholders from Rule #1. Fill in the carried digits, the answer and the decimal point, and check your work as often as you like.
Small red boxes: carried digits (leave a box empty if nothing is carried). Boxes below the line: the answer, with a narrow box for the decimal point.