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Multiplying and dividing decimals

Multiplying and dividing decimals

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Explainer Video

Tutor: Alice

Summary

Multiplying and dividing decimals

​​In a nutshell

A decimal can be expressed as a whole number divided by a power of 101010. Multiplication and division with decimals can be made simpler by using whole numbers and then applying this same division at the end.



Multiplication with decimals

There are two methods that can be used to multiply using decimals.


Method 1

procedure

​​1.

Count how many digits are to the right of the decimal point in each number and add to get the total.​

2.

Remove the decimal and multiply the numbers as if they were whole numbers.​

3.

Move the decimal point to the left of the units digit of the answer by the same number.

​

Example 1

​What is 0.53×2.210.53 \times 2.210.53×2.21?


Count how many digits are to the right of the decimal point in total.

0.5‾ 3‾→22.2‾ 1‾→22+2=40.\underline{5}\space\underline{3}\rightarrow 2 \\2.\underline{2}\space\underline{1}\rightarrow2\\2+2=40.5​ 3​→22.2​ 1​→22+2=4


Remove the decimals from 0.530.530.53 and 2.212.212.21 and multiply as if they were whole numbers.

53×221=11 71353\times221=11\space71353×221=11 713​​


Move the decimal point four spaces to the left.

11713. ↶↶↶↶1. 1713\\1\enspace1 \enspace7\enspace1\enspace3.\\\enspace\space\curvearrowleft \curvearrowleft\curvearrowleft\curvearrowleft\enspace\\1.\space1 \enspace7\enspace1\enspace3\\11713. ↶↶↶↶1. 1713​ 


​0.53×2.21=1.1713‾0.53\times2.21=\underline{1.1713}0.53×2.21=1.1713​​​

​

Method 2

​​Procedure

1.

Rewrite each decimal as a whole number divided by a 10,10010,10010,100​ etc.

2

Multiply the whole numbers together.

3.

Divide the result by the same powers of 101010​ that the whole numbers were originally divided by.

​

Note: You can use any method to multiply whole numbers, whether it be using a calculator, using the column method, or using the grid method.


Example 2

What is 0.5×42.10.5 \times 42.10.5×42.1?


Rewrite the decimals as whole numbers divided by powers of 101010.

0.5=5÷1042.1=421÷100.5=5\div10\\42.1=421\div100.5=5÷1042.1=421÷10


Multiply the whole numbers together.

421×5=2105421\times5=2105421×5=2105


Divide by 101010 and 101010.

2105÷10÷10=21.05‾2105\div10\div10=\underline{21.05}2105÷10÷10=21.05​​​

​

Note: When multiplying decimals, your final answer should always have the same total number of decimal places as the sum of of the number of decimal places you started with.



Division with decimals

Dividing using decimals also involves two methods: one being a very similar method to multiplication.


Method 1

​​Procedure

1.

Rewrite each decimal as a whole number divided by a power of 101010.

2.

If the divisor is a decimal then the division of the power of 101010​ turns into multiplication.​

2.

Complete the division of the whole numbers by using a calculator or short division (where required).

4.

Divide/multiply the final answer accordingly.


Example 3

What is 0.132÷1.10.132 \div 1.10.132÷1.1?


Rewrite each decimal as a whole number divided by a power of 101010.

0.132=132÷10001.1=11÷100.132=132\div1000\\1.1=11\div100.132=132÷10001.1=11÷10​​

​​

The divisor in this case is 1.11.11.1 so turn its ÷10\div10÷10 into ×10\times 10×10 and divide.

132÷11=12132\div11=12132÷11=12


Divide by 100010001000 and multiply by 101010.

12÷1000×10=0.1212\div1000\times10=0.1212÷1000×10=0.12​​

​​

0.132÷1.1=0.12‾\underline{0.132\div1.1=0.12}0.132÷1.1=0.12​​​


Method 2

Simply multiply the dividend and divisor by the same power of 101010 until both are whole numbers and divide as usual.


Example 4

What is 0.99÷0.90.99\div0.90.99÷0.9?


Multiply by the same powers of 101010 until both are whole.

0.99×100=990.9×100=900.99\times100=99\\0.9\times100=900.99×100=990.9×100=90


Divide 999999​ by 909090.

​90)9 99.90 ‾ 1 . 1 90\overset{\,\,\,\,\,\,\,\,\,\,1\,.\,\,\,1\,\,}{\overline{\smash{)}\cancel9\space^99.^90\,\,\,}} \\ 90)9​ 99.901.1​​


​0.99÷0.9=1.1‾\underline{0.99\div0.9=1.1}0.99÷0.9=1.1​​​

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Multiplying decimals by whole numbers

Multiplying decimals by whole numbers

Methods for multiplication and division

Methods for multiplication and division

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Multiplying and dividing decimals

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FAQs - Frequently Asked Questions

Where do we use decimals in real life?

We use decimals every day while dealing with money, weight, length etc. Decimal numbers are used in situations where more precision is required than the whole numbers can provide.

What strategies do you use when multiplying decimals?

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

What are the rules for multiplying and dividing decimals?

When multiplying decimals, the number of decimal places in the product is the sum of the decimal places in the factors. When dividing by decimals, move the decimal point in the dividend the same number of places to the right as you move the decimal point in the divisor.

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