Multiplying decimals is very similar to multiplying whole numbers. You multiply the digits exactly the same way. The only new step is putting the decimal point in the right place at the end.
Rule #1: Ignore the decimal points and multiply the numbers as if they were whole numbers. For 2.4 × 1.3, multiply 24 × 13.
Rule #2: Count the decimal places (the digits to the right of the decimal point) in each factor, and add them. 2.4 has 1 decimal place and 1.3 has 1, so the product needs 1 + 1 = 2 decimal places.
Rule #3: Start at the right end of the whole-number product and count that many digits to the left. Put the decimal point there. 24 × 13 = 312, so 2.4 × 1.3 = 3.12.
Don't line up the decimal points the way you do when adding. When you multiply, the decimal points don't need to be lined up at all. You only count decimal places at the end.
How many decimal places does the product of 6.25 × 0.4 have?
3. 6.25 has 2 decimal places and 0.4 has 1, and 2 + 1 = 3. (625 × 4 = 2,500, so 6.25 × 0.4 = 2.500 = 2.5.)
| 1 | |||
| 2. | 4 | ||
| × | 1. | 3 | |
| 7 | 2 | ||
| + | 2 | 4 | 0 |
| 3. | 1 | 2 |
2.4 × 1.3 = 3.12
Example 2: Multiply 3.25 × 4
| 1 | 2 | |||
| 3. | 2 | 5 | ||
| × | 4 | |||
| 1 | 3. | 0 | 0 |
Multiply 325 × 4 = 1,300.
3.25 has 2 decimal places and 4 has none, so the product has 2 decimal places.
Count 2 digits from the right of 1300: 13.00
3.25 × 4 = 13.00 = 13
The zeros at the end after the decimal point can be dropped: 13.00 = 13. Always count them first, though, so that the decimal point goes in the right place.
A quick check: 2.4 × 1.3 is a little more than 2 × 1 = 2 and less than 3 × 2 = 6, so 3.12 makes sense. An answer like 31.2 or 0.312 would not.
Multiply 1.5 × 0.7.
1.05. 15 × 7 = 105. There are 1 + 1 = 2 decimal places, so the product is 1.05.
Sometimes the whole-number product doesn't have enough digits for all the decimal places. Then write zeros in front of it until there are enough digits, and put a 0 before the decimal point.
Example 3: Multiply 0.3 × 0.02
Multiply 3 × 2 = 6.
0.3 has 1 decimal place and 0.02 has 2, so the product needs 1 + 2 = 3 decimal places.
6 has only 1 digit, so write two zeros in front: 006.
Put the decimal point 3 digits from the right: .006
0.3 × 0.02 = 0.006
0.3 × 0.2 is not 0.6. The product needs 1 + 1 = 2 decimal places, so 0.3 × 0.2 = 0.06. Multiplying two numbers smaller than 1 gives an even smaller number.
Multiply 0.4 × 0.12.
0.048. 4 × 12 = 48. There are 1 + 2 = 3 decimal places, so write one zero in front: 0.048.
In each problem you multiply the whole numbers in the grid first, then put the decimal point in the answer. Problem 1 guides you through every step. Problem 2 uses fewer, bigger steps, with a hint for each one. Problem 3 has no step-by-step help: you fill in the whole grid and place the decimal point yourself, with one hint per step if you need it. You can skip a problem at any time, and each time you play you get new problems.
Practice Complete!
Type two decimals (or a decimal and a whole number), each with up to 3 decimal places. Without the decimal point, the first number can have up to 4 digits and the second up to 3. Make your grid, multiply the whole numbers, then type the answer with the decimal point. The "Carries" lines are there to help you; you don't have to fill them in.
The label on the left of each line of boxes says what goes in it.