 The Logic Behind the Method
 The Method of Multiplying Decimals
 Calculators
 Multiplying Decimals By Powers of 10
 Multiplication in Terms of “Of”
Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to multiply decimals. By the end of the module students should understand the method used for multiplying decimals, be able to multiply decimals, be able to simplify a multiplication of a decimal by a power of 10 and understand how to use the word "of" in multiplication.
Consider the product of 3.2 and 1.46. Changing each decimal to a fraction, we have
Thus,
Notice that the factor
Using this observation, we can suggest that the sum of the number of decimal places in the factors equals the number of decimal places in the product.
To multiply decimals,
Find the following products.
Thus,
Thus,
Find the product of 0.251 and 0.00113 and round to three decimal places.
Now, rounding to three decimal places, we get
Find the following products.
45.58
10.388
0.16864
0.00000062
Find the product of 2.33 and 4.01 and round to one decimal place.
9.3
53.94
539.4
5,394
59,340
Calculators can be used to find products of decimal numbers. However, a calculator that has only an eightdigit display may not be able to handle numbers or products that result in more than eight digits. But there are plenty of inexpensive ($50  $75) calculators with more than eightdigit displays.
Find the following products, if possible, using a calculator.
Display Reads  
Type  2.58  2.58 
Press  ×  2.58 
Type  8.61  8.61 
Press  =  22.2138 
The product is 22.2138.
Display Reads  
Type  .006  .006 
Press  ×  .006 
Type  .0042  0.0042 
Press  =  0.0000252 
We know that there will be seven decimal places in the product (since
Since we expect
Display Reads  
Type  .0026  .0026 
Press  ×  .0026 
Type  .11976  0.11976 
Press  =  0.0003114 
Rounding 0.0003114 to three decimal places we get 0.000. Thus,
Use a calculator to find each product. If the calculator will not provide the exact product, round the result to four decimal places.
20.91408
0.000066
0.2397
0.0000
There is an interesting feature of multiplying decimals by powers of 10. Consider the following multiplications.
Multiplication  Number of Zeros in the Power of 10  Number of Positions the Decimal Point Has Been Moved to the Right 

1  1 

2  2 

3  3 

4  4 
To multiply a decimal by a power of 10, move the decimal place to the right of its current position as many places as there are zeros in the power of 10. Add zeros if necessary.
Find the following products.
Since there is no fractional part, we can drop the decimal point.
Find the following products.
427
165,218.7
0.188
527,000,000,000
Recalling that the word "of" translates to the arithmetic operation of multiplication, let's observe the following multiplications.
Find 4.1 of 3.8.
Translating "of" to "×", we get
Thus, 4.1 of 3.8 is 15.58.
Find 0.95 of the sum of 2.6 and 0.8.
We first find the sum of 2.6 and 0.8.
Now find 0.95 of 3.4
Thus, 0.95 of
Find 2.8 of 6.4.
17.92
Find 0.1 of 1.3.
0.13
Find 1.01 of 3.6.
3.636
Find 0.004 of 0.0009.
0.0000036
Find 0.83 of 12.
9.96
Find 1.1 of the sum of 8.6 and 4.2.
14.08
For the following 30 problems, find each product and check each result with a calculator.
31.28
47.20
0.152
4.6324
3.182
0.0000273
2.56
0.81
29.3045
0.00000105486
49.6
4,218.842
19.621
3,596.168
25,010
Actual product  Tenths  Hundreds  Thousandths 
Actual product  Tenths  Hundreds  Thousandths 
28.382  28.4  28.38  28.382 
Actual product  Tenths  Hundreds  Thousandths 
Actual product  Tenths  Hundreds  Thousandths 
Actual product  Tenths  Hundreds  Thousandths 
134.216048  134.2  134.22  134.216 
Actual product  Tenths  Hundreds  Thousandths 
Actual product  Tenths  Hundreds  Thousandths 
Actual product  Tenths  Hundreds  Thousandths 
185.626  185.6  185.63  185.626 
For the following 15 problems, perform the indicated operations
Find 5.2 of 3.7.
Find 12.03 of 10.1
121.503
Find 16 of 1.04
Find 12 of 0.1
1.2
Find 0.09 of 0.003
Find 1.02 of 0.9801
0.999702
Find 0.01 of the sum of 3.6 and 12.18
Find 0.2 of the sum of 0.194 and 1.07
0.2528
Find the difference of 6.1 of 2.7 and 2.7 of 4.03
Find the difference of 0.071 of 42 and 0.003 of 9.2
2.9544
If a person earns $8.55 an hour, how much does he earn in twentyfive hundredths of an hour?
A man buys 14 items at $1.16 each. What is the total cost?
$16.24
In the problem above, how much is the total cost if 0.065 sales tax is added?
A river rafting trip is supposed to last for 10 days and each day 6 miles is to be rafted. On the third day a person falls out of the raft after only
0.24
A woman starts the day with $42.28. She buys one item for $8.95 and another for $6.68. She then buys another item for sixty twohundredths of the remaining amount. How much money does she have left?
For the following 10 problems, use a calculator to determine each product. If the calculator will not provide the exact product, round the results to five decimal places.
0.006099
23.295102
0.000144
0.0000018
0.0000000471
((Reference)) Find the value, if it exists, of
0
((Reference)) Find the greatest common factor of 210, 231, and 357.
((Reference)) Reduce
((Reference)) Write "fourteen and one hundred twentyone tenthousandths, using digits."
((Reference)) Subtract 6.882 from 8.661 and round the result to two decimal places.
1.78
"Used as supplemental materials for developmental math courses."