Math 40
Prealgebra
Section 5.3 – Multiplying Decimals
5.3 Multiplying Decimals
Multiplying Decimals
1. Ignore the decimal points and find the product of the two factors as if they
were whole numbers (ie. line the numbers up on the right and multiply as
shown in Section 1.3)
2. Find the total number of digits behind the decimal points. (ex. When
multiplying  3.25  57.167  , we have 2 digits behind the decimal point in
the first number and 3 digits behind the decimal point in the second number.
Therefore the total number of digits behind the decimal points is 5.
3. In your product from Step 1, place a decimal point so that there is the same
number of digits behind the decimal point as your total in Step 3.
Example 1: Multiply.
 2.34 1.2 
Solution: Step 1) Ignore the decimal points and multiply.
234
 12
468
 2340
2808
Step 2) Count the total number of digits behind the decimal points.



2 digits + 1 digit = 3 digits
 2. 34   1. 2 
 2 digits   1 digit 
Step 3) Place the same number of digits (from step 2) behind a decimal point in your answer from
step 1.
2. 808
3 digits
Therefore,  2.34 1.2   2.808
You Try It 1: Multiply.
 5.98  3.7 
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Math 40
Prealgebra
Section 5.3 – Multiplying Decimals
Example 2: Multiply.  8.235  2.3 
Solution: Step 1) Ignore the decimal points and multiply.
8235
 23
24705
 164700
189405
Step 2) Count the total number of digits behind the decimal points.



3 digits + 1 digit = 4 digits
 8. 235   2. 3 
 3 digits   1 digit 
Step 3) Place the same number of digits (from step 2) behind a decimal point in your answer from
step 1.
18.9405
4 digits
Therefore,  8.235  2.3   18.9405
You Try It 2: Multiply.
 9.582  8.6 
Note: To simplify the multiplying decimal process, we will keep the decimals in the
numbers when we stack them vertically to multiply. We will then count the total number
of decimal places and use that in our answer.
Review of Multiplying Signed Numbers
Like Signs: The product to two numbers with like signs is positive.
      
      
Unlike Signs: The product to two numbers with unlike signs is negative.
      
      
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2015 Worrel
Math 40
Prealgebra
Section 5.3 – Multiplying Decimals
Example 3: Multiply.
 2.22  1.23 
Solution: Since the two numbers are both negative (they have like signs), we know our answer is positive.
2.22
 1.23
666
4440
 22200
2.3306
Therefore,  2.22  1.23  2.3306
You Try It 3: Multiply.
Example 4: Multiply.
 3.86  5.77 
 5.68  0.012 
Solution: Since the two numbers have unlike signs, we know our answer is negative.
5.68
 0.012
1036
 5680
0.06716
Therefore,  5.68  0.012   0.06716
You Try It 4: Multiply.
 9.23 0.018 
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Math 40
Prealgebra
Section 5.3 – Multiplying Decimals
Powers of Ten
Consider:
101  10
(1 followed by ONE zero)
102  10 10  100
(1 followed by TWO zeros)
10  10 10 10  1000
3
(1 followed by THREE zeros)
10  10 10 10 10  10, 000
4
(1 followed by FOUR zeros)
Powers of Ten
In the expression 10n , the exponent matches the number of zeros in the answer. Hence, 10n will
be a 1 followed by n zeros.
Example 5: Simplify. 109
Solution: According to the Powers of Ten rule above, 109 should be a 1 followed by NINE zeros.
109  1, 000, 000, 000
You Try It 5: Simplify. 106
Multiplying by Powers of Ten
Consider:
1.234567 101  12.34567
1.234567 10 2  123.4567
1.234567 103  1, 234.567
1.234567 10 4  12,345.67
Multiplying by Powers of Ten
Multiplying a number by 10n will move the decimal point n places to the right.
EX: 23.58941104  23.5894.1  235,894.1
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2015 Worrel
Math 40
Prealgebra
Section 5.3 – Multiplying Decimals
Example 6: Simplify. 1.234567 105
Solution: According to the Multiplying by Powers of Ten rule, multiplying by 105 should move the decimal
point FIVE places to the right.
1.234567 105  1.23456.7  123, 456.7
You Try It 6: Simplify. 1.234567 106
Example 7: Simplify. 1.234567 109
Solution: According to the Multiplying by Powers of Ten rule, multiplying by 109 should move the decimal
point NINE places to the right. If you run out of digits at the end, remember to add zeros.
1.234567 109  1.234567000.  1, 234,567, 000
You Try It 7: Simplify. 1.234567 107
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