Topic
multiplication of Decimal
Objective
To find the product of the given decimal
pre-requisite knowledge
1. Representation of decimals
2. Multiplication of numbers
procedure
1. Let us assume that we wish to multiply 0.6 and 0.5
2. Represent 0.6 horizontally and 0.5 vertically on two different O. H. P. as shown in the figures given below
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Answers
Step-by-step explanation:
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 a decimal by a whole number
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.
Example
Working out
Regrouping
Answer
3 x 8 = 24
Three groups of eight ones is 24 ones.
24 ones is the same as 2 tens and 4 ones.
24
3 x 0.8 = 2.4
Three groups of eight tenths is 24 tenths.
24 tenths is the same as 2 ones and 4 tenths.
2.4
3 x 0.08 = 0.24
Three groups of eight hundredths is 24 hundredths.
24 hundredths is the same as 2 tenths and 4 hundredths.
0.24
3 x 0.008 = 0.024
Three groups of eight thousandths is 24 thousandths.
24 thousandths is the same as 2 hundredths and 4 thousandths.
0.024
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:
1/10 x 8/10 = 8/100 = 0.08 (using rules for fraction multiplication)
0.1 x (0.1 x 8) = 0.01 x 8 = 0.08 (using rules for decimal multiplication)
one tenth of eight tenths is eight hundredths (using common sense)
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.