This article looks in detail at how to multiply decimals, such as 1.5 times 7. We will explain how to multiply decimals by the power of 10 (e.g. 10, 100, 1000), multiply by another decimal and multiply by a whole number. Decimal multiplication is common in Maths so we have included plenty of examples for you to see the calculation breakdown. There are also questions to grade your knowledge. If you need further support in your Maths education, you can search for KS3 Maths lessons.
Decimal multiplication by 10, 100, 1000, etc
First things first, in Maths a decimal is any number that is not a whole number. For example, 0.58 and 4.6 are decimals.
To multiply decimals, it's important that we use the powers of ten. Every time we multiply by a power of ten, we put the decimal point a place to the left and every digit in the number increases in place value. For example, if we multiply 0.01 by the power of ten once, it becomes 0.1 (0.01 x 10 = 0.1).
The same is true if we are dividing decimals - dividing by 10 moves the decimal point place to the right each time and the place value of each digit decreases. For example, the place value of the digits in 135.25 is 1 hundred, 3 tens, 5 units, 2 tenths and 5 hundredths. If we divide 135.25 by 1000, the decimal point moves three places to the left (135.25 / 1000 = 0.13525). This means the place value of each digit has also changed (1 tenth, 3 hundredths, 5 thousandths etc).
Decimal examples - Multiply by the powers of 10
Multiply 0.025 by 10:
- Write the number using its place value labels: 2 hundredths, 5 thousandths.
- To multiply by 10 once, we need to move the decimal point one to the right. The place value of 2 hundredths will change to 2 tenths and 5 thousandths will change to 5 hundredths.
- 0.94 x 10 = 0.94
Multiply 2.56 by 100:
- Write the number using its place value labels: 2 units, 5 tenths, 6 hundredths.
- Multiplying by 100 means multiplying to the power of 10 twice (10 x 10). This means we need to move the decimal point two to the right. The place value for each digit will change to 2 hundreds, 5 tens and 6 units.
- 2.56 x 100 = 256
Multiply 0.591 by 1000:
- Write the number using its place value labels: 5 tenths, 9 hundredths, 1 thousandth.
- Multiplying by 1000 means multiplying to the power of 10 three times (10 x 10 x 10). This means we need to move the decimal point three places to the right. The place value for each digit will change to 5 hundreds, 9 tens and 1 unit.
- 0.591 x 1000 = 591
Solve 4.25 x 100
It's helpful to make sure that the total number of decimal digits in the question matches the total number in the answer e.g. 2.35 times 3 = 7.05. Both the original value and the answer have two decimal digits so this is correct. Remember that you then must remove any zeros from the end of the answer.
How to multiply decimals by a whole number
To multiply a decimal, we need to multiply by powers of ten to turn all digits into whole numbers. We then do the multiplication with the new whole number. Finally, we divide by the same powers of ten to get the final answer. It may help to think of it a different way: ignore the decimal and then add it back at the end:
- Multiply the decimal by the powers of ten needed to turn it into a whole number. For example, the number of decimal places for 2.35 is two so it needs to be multiplied by the powers of ten twice (2.35 x 10 x 10 = 235).
- Multiply the whole number by the value given (if the question is 2.35 x 4, this will now be 235 x 4). Use any of the following multiplication methods: short multiplication, the area method, the Partition method, or Napier's method (235 x 4 = 940).
- Use division on the product by the powers of ten used in step 1 (940 / 10 / 10 = 9.40).
- Remove any unnecessary zero digits from the answer (9.40 = 9.4).
Follow the link if you'd like more information about the powers of ten in a detailed article by Wikipedia.
Decimal examples - Multiply by a whole number
Multiply 23.4 by 5:
- Multiply 23.4 by the power of ten once to turn it into a whole number (23.4 x 10 = 234).
- We can now multiply without the decimal point (234 x 5 = 1170)
- Divide the product by the power of ten once (1170 / 10 = 117.0)
- Remove any zero digits from the end (117.0 = 117)
Multiply 78.43 by 9:
- First multiply 23.4 by the power of ten twice to turn it into a whole number (78.43 x 10 x 10 = 7843).
- Complete the calculation with the new whole number (7843 x 9 = 70587)
- Divide the product by the power of ten twice (70587 / 10 / 10 = 705.87)
- Remove any zero digits from the end (N/A)
Solve 5 x 8.2
Multiply decimals by another decimal
Multiplying a decimal by another decimal is almost the same as multiplying by a whole number. Really, the only difference is that in addition, we will be multiplying both numbers by the powers of ten. Then, after the calculation, we divide the answer from the combined powers of ten:
- Turn each decimal into a whole number by multiplying by the powers of 10. For example, the question is 3.45 x 5.7. The first decimal has two decimal digits - it needs to be multiplied to the power of ten twice (3.45 x 10 x 10 = 345). The second decimal is only multiplied once (5.7 x 10 = 57).
- Next, multiply both whole numbers together (345 x 57 = 19665).
- Divide the answer by the combined powers of ten exponents in step 1 (there were 2 powers of ten for 3.45 and 1 for 5.7 so the combined exponent of the power of ten is 3. Therefore, 19665 / 10 / 10 / 10 = 19.665)
- Remove any zero digits from the end of the number.
- Decimal example - Multiply by another decimal
Decimal example - Multiply by another decimal
Multiply 14.7 by 4.68:
- Multiply 14.7 by the power of ten once to turn it into a whole number (14.7 x 10 = 147). 4.68 also has two decimal digits and needs to be multiplied by the power of ten twice (4.68 x 10 x 10 = 468).
- Complete the calculation with both new whole numbers (147 x 468 = 68796)
- The first decimal was multiplied by the powers of ten once, the second decimal was multiplied twice. Combine them and divide the number to the powers of ten three times (68796 / 10 / 10 / 10 = 705.87)
- Remove any zero digits from the end of the number (N/A).
Work out 6.31 x 25.75:
- Multiply 6.31 by the power of ten twice (6.31 x 10 x 10 = 631) and multiply 25.75 by the power of ten twice (25.75 x 10 x 10 = 2575).
- Complete the calculation with both new whole numbers (631 x 2575 = 1624825)
- Both decimals were multiplied by the power of ten twice so the combined exponent is 4. Divide the calculation by the powers of ten four times (1624825 / 10 / 10 / 10 / 10 = 162.4825)
- Remove any zero digits from the end of the number (N/A).
Multiply 24.3 and 9.2
- place value - The value of a digit depending on its position inside a number. For example, the place value of the digit 5 in the number 151 is 5 tens. The place value for each digit in the number is 1 hundred, 5 tens and 1 unit.
- integer - A whole number, such as 3. An integer can be positive or negative. Zero also counts as an integer.
- powers of 10 - This means to multiply 10 by itself as many times as stated. For example, 102 equals 100 (10 x 10) and 103 equals 1000 (10 x 10 x 10). Powers of 10 begin with 10, 100, 1000, 10000 and so on.
- product - This is the answer when you multiply two numbers together. For example, the product of 2 and 8 is 16 (2 x 8 = 16).
This post was updated on 01 Aug, 2023.