Multiplication of decimals relies on knowing how to multiply whole numbers, understanding place value, and appreciating the various multiplication situations involving decimals. The endless base ten chain shows the consistency of the base ten place value system from whole numbers to decimals.
As with whole number multiplication, the order of the numbers being multiplied does not affect the product. This is called the commutative property of multiplication.
Multiplying decimals relies on adapting multiplication of whole numbers. When one of the numbers being multiplied is reduced to a tenth of its original size, the product is also reduced to a tenth of its original size. The following chart demonstrates this relationship.
Multiplying decimals by decimals
When multiplying a number by a decimal less than one, the product will be smaller than the number being multiplied. This is because we are finding a fractional amount of a quantity. For example, 0.1 x 0.8 = 0.08, because the question is asking us to find one tenth of eight tenths. A tenth of a tenth (or a tenth multiplied by a tenth) is a hundredth, thus one tenth of eight tenths is eight hundredths.
Viewing decimal multiplication problems in common fraction and extended decimal form may help us better understand the answer. We can link multiplication of decimals to common fractions because we know that 0.1 (one tenth) is the same as 1/10, or 1 ÷ 10. Similarly, we can expand the way we record decimals to gain an understanding of the size of answers because we know that 0.1 is the same as 1 x 0.1, or 1 ÷ 10. We can rewrite 0.1 x 0.8 as:
The relationship between the place value of the numbers being multiplied and the product is summarised by the following chart. As we move to the right or down the chart, the numbers increase by a factor of ten, so the answers increase by a factor of ten.
common way to multiply decimals is to treat them as whole numbers,
and then position the decimal point in the product. The number of
digits after the decimal points in the factors determines where the
decimal point is placed in the answer.
Example 1: Full explanation of 1.8 x 2.3 = 4.14
A wire expands to 1.8 times its length when heated. The wire is 2.3 cm long. How long will it be when heated?
Example 2: Placing the decimal point, 23 x 0.67 = 15.41
costs $0.67 per litre. Khumalo pumps 23 litres of petrol into his
car. How much does it cost him? To find this out I need to multiply
23 litres by $0.67. 0.67 is over half of one dollar, so my answer
will be over $11 (half of $22).
Example 3: Full explanation of 0.234 x 0.07 = 0.01638
Rows of zeros contribute nothing to the final answer and therefore are a waste of time and ink. The decimal point can be placed without multiplying the rows of zeros. 234 x 7 is 1638, but 0.237 x 0.07 will have 5 decimal places in the answer, so it will be 0.01638.
Caution: if you use the rule of counting decimal places in the question to find the number of decimal places in the answer, you MUST not discard zeros too early. For example, to multiply 0.25 by 0.4, you need 2+1 decimal places and the multiplication without a decimal point gives 0100. The answer is therefore 0.100. This is equal to 0.1, but the right-most decimal places cannot be discarded until after the multiplication rule has been used.
1. Given that 4857 x 6 = 29142, find:
1. Find the product of 7.15 and 1.9
2. Evaluate 7.04 x 1.1
3. Steves stride is 84.6 cm. How many centimetres will he travel if he takes 200 strides?
4. The length of my front garden bed is 4.3 times longer than the length of my back garden bed. If the length of my back garden bed is 156 cm, how long is my front garden bed?
Is the following statement true or false: 9.6734 x 0.9 > 9.6734?
To view the quiz answers, click here.
If you would like to do some more questions, click here to go to the mixed operations quiz at the end of the division section.
University of Melbourne