Multiplying with decimals

It is important that your children gain an understanding of place value when multiplying decimals. Below are examples to help develop this understanding. They include the use of place value charts with counters, Base-10 blocks, and an area model.

Examples Showing Multiplication of Decimals

On a Place Value Chart

0.4 x 2

four tenths multipled by 2 illustrated on a place value chart with counters

0.21 x 3

twenty-one hundredths multipled by 3 illustrated on a place value chart with counters

The first two examples above do not require regrouping although those that follow do. Your children should build on their understanding of whole number place vale and be able to see that, for example, 13 hundredths can be regrouped as 1 ten and three hundredths, and that 17 tenths can be regrouped as 1 whole unit and 7 tenths.

Help your children to model decimal multiplication using counters on a place value chart regrouping 10 smaller units as one unit ten times larger. You can follow the examples below or you can create your own. You will find a printable place value chart here.

0.4 x 3

four tenths multipled by 3 illustrated on a place value chart with counters

0.62 x 3

sixty-two hundredths multipled by 3 illustrated on a place value chart with counters

0.317 x 5

three hundred seventeen thousandths multipled by 5 illustrated on a place value chart with counters

Using Base-10 Blocks

If you have Base-10 blocks then they can be used to model multiplication and regrouping as shown in the examples below.

1.6 x 2

one and six tenths multipled by 2 illustrated with Base-10 blocks

0.27 x 2

twenty-seven hundredths multipled by 2 illustrated with Base-10 blocks

0.74 x 3

seventy-four hundredths multipled by 3 illustrated with Base-10 blocks

Area Method For Multiplication

The area method for multiplication, more on which you will find here with whole numbers, can be used to show and model decimal multiplication as the examples below show.

0.23 x 3

twenty-three hundredths multipled by 3 calculated using the area method

0.212 x 4

two hundred twelve thousandths multipled by 4 calculated using the area method

0.317 x 5

three hundred seventeen thousandths multipled by 5 calculated using the area method

Rounding, Estimating, and Checking

The location of the decimal point in any answer is vitally important and it can be easily misplaced. Estimating an answer by rounding the multiplier and/ or multiplicand and performing a quick mental or written check can help to determine if the answer is reasonable.

3.65 x 4 in a thought bubble with the words suggesting 3.65 is between 3 and 4 so the answer is expected to be between 12 and 16

Multiplying Decimals by Powers of 10

The table below shows examples of decimals multiplied by powers of 10. Encourage your children to identify patterns in the placement of the decimal point, the number of zeros, and the power of 10 by which the decimal is multiplied. There is more here on decimals being multiplied by powers of 10.

5.23 x 101 = 52.3 0.174 x 105 = 17,400
5.23 x 102 = 523 0.174 x 104 = 1,740
5.23 x 103 = 5,230 0.626 x 106 = 626,000
0.26 x 103 = 260 0.626 x 105 = 62,600
0.19 x 102 = 190 0.626 x 104 = 6,260

Multiplying Decimals - Algorithm

Explain to your child that multiplying decimals is similar to multiplying with whole numbers. The main difference is that the number of decimal places in the answer must be the same as the total number of decimal places in the question. You can use the idea of hops instead of decimal places.

When tutoring your children on decimals be sure to explain the real-life relevance of multiplication with decimals. Money is usually an idea that children can identify with. e.g. if you get $5.50 every week for 8 weeks, how much will you have at the end of the eight weeks?

Illustration of multiplication of two decimal numbers with the idea of hops being counted to locate the decimal point in the answer.:

Common Error When Multiplying Decimals

The example below highlights are fairly common mistake that students make when multiplying decimals.

example showing mistake when multiplying decimals

"Using the wrong rule" type errors are best dealt with by discussing the underlying principles. This will require a solid understanding of place value and knowing that moving the decimal point one place is equivalent to multiplying or dividing by 10 depending on the direction of movement.

This error also highlights the benefits of estimating the answer to check whether the calculated answer is reasonable.

Caution: When multiplying decimals by 10 or multiples on 10, beware of your children applying the dangerous, "just add a zero" rule that is associated with multiplying by 10 - it can cause mistakes like 1.2 x 10 = 1.20

Worksheets

happy face iconHave a go at the decimals worksheet generator. It provides limitless multiplying decimals questions. Note: This generator also provides adding and subtracting decimal questions as well.

There is also another generator just for multiplying decimals and it allows decimals to be multiplied by multiples of 10 and of 100.

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