Transcript Section 3.4 Notes

Chapter 3
Decimals
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
3.4
Multiplying Decimals
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplying Decimals
The multiplication of decimals is related to the multiplication
of fractions. 3
4
12

10 100

1000
0.3 0.04  0.012
one
decimal
place
two
decimal
places
three
decimal
places
Multiplying Decimals
1.
2.
3.
Multiply the numbers just as you would multiply whole
numbers.
Find the sum of the decimal places in the two factors.
Place the decimal point in the product so that the
product has the same number of decimal places as the
sum in step 2. You may need to write zeros to the left of
the number found in step 1.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplying Decimals
Example:
Multiply 0.17  0.4.
0.17
 0.4
0.068
2 decimal places
1 decimal place
3 decimal places in product (2 + 1 = 3)
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplying Decimals
Example:
Multiply 0.043  0.012.
0.043 3 decimal places
 0.012 3 decimal places
86
43
0.000 516 6 decimal places in product (3 + 3 = 6)
Note the we need to
insert three zeros
before the 516.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplying by a Power of 10
Observe the following pattern.
one zero
Decimal point moved
one place to the right.
0.025  101 = 0.025  10 = 0.25
two zeros
Decimal point moved
two places to the right.
0.025  102 = 0.025  100 = 2.5
three zeros
Decimal point moved
three places to the right.
0.025  103 = 0.025  1000 = 25
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplying by a Power of 10
Multiplication of a Decimal by a Power of 10
To multiply a decimal by a power of 10, move the decimal
point to the right the same number of places as the number of
zeros in the power of 10.
Example:
Multiply 4.59  10,000.
4.59  10,000 = 45,900
four zeros
Decimal point moved
four places to the right.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.