Multiplication of Decimals   General Multiplication of Decimals The rules for multiplication of decimals come from the rules of multiplying fractions.  Consider the product         0.02 x 0.013 in fraction form this is             2                13               26                       x                =                   =  0.00026             100           1000          100000 Notice that the denominator is found by adding the two zeros from the first denominator to the three zeros of the second denominator.  In decimal notation, we can see that there are 2 digits to the right of the first decimal point and three digits to the right of the second decimal point.  The result has 2 + 3 = 5 digits to the right of the decimal point. In general to multiply two decimal numbers, follow the steps below Step 1    Multiplying the numbers ignoring the decimal points. Step 2    Add the number of digits to the right of the decimal points. Step 3    Place the decimal point so that the number of digits to the right is the result of part 2. Example         0.04 x 0.3 Solution 4 x 3  =  12 2 + 1  =  3    0.04 has 2 digits to the right and 0.3 has one digit to the right 0.012        0.012 has 3 digits to the right of the decimal point Example         1.02 x 0.016 Solution        102     x 16      612 + 1020     1632 2 + 3 = 5 0.01632   Example         2.3 x 47 Solution           2            1        23     x 47      161   + 920     1081 1 + 0 = 1    A whole number has 0 decimal digits. 108.1 Exercises     Multiply the following decimals 0.32 x 0.0006        8.13 x 39          Multiplying a Decimal by a Power of 10 Consider the multiplication problem         0.00034 x 100 In fractions this becomes                   34                   1 100            34                                     x                =                   =  0.034             1000 100000              1             1000 Notice that we canceled 2 zeros in the fraction.  This results in moving the decimal point over to the right two places.   In General When multiplying a decimal by a power of 10, move the decimal to the right the same number of places as the number of zeros of the power of 10. Example Multiply 3.416 x 100 Solution Since there are two zeros in 100, we move the decimal two places to the right         3.416 x 100    =  341.6 Example Multiply         2.05 x 10,000     Solution Since there are four zeros in 10000, we move the decimal four places to the right.  In order to do this, pad 2.05 with 2 extra zeros first.         2.05  =  2.0500         2.0500 x 10,000    =  20,500 Exercises Multiply 34.30541 x 1000    97.51 x 100,000    Applications Example How many meters is 3.4 kilometers Solution We use the fact that there are 1000 meters in 1 kilometer.  This becomes a multiplication problem involving a power of ten         3.4 x 1000  =  3.400 x 1000  =  3,400 There are 2,100 meters in 2.1 kilometers. Example You just bought a 2.1 gigahertz Intel processor. How many hertz is this given that one gigahertz is 1,000,000,000 hertz.  We multiply, noting that this is a power of 10.         2.1 x 1,000,000,000  =  2.100000000 x 1,000,000,000          =  2,100,000,000 The processing power is 2,100,000,000 hertz (two billion one hundred million hertz). Example You have just bought 3.2 pounds of rib eye steak at \$2.89 per pound.  What will the steak cost you? Solution This is the multiplication problem 2.89 x 3.2.          289       x   32          578     + 8670        9248 Adding decimal digits gives          2 + 1  =  3 2.89 x 3.2  =  9.248 Since this is a money problem, we should round to the nearest cent, which gives         \$9.25 The steak will cost \$9.25. Example You have just bought a building on highway 50 that has a rectangular dance floor of dimensions 10.3 feet by 11.2 feet.  What is the square area of the dance floor? Solution Recall that the area of a rectangle is the length times the width.  We multiply             112         x  103             336      + 11200         11536 Adding decimal digits gives         1 + 1  =  2 The floor is 115.36 square feet Exercises How many grams are there in 5.42 kilograms?    Your car achieves 24.5 miles per gallon on the highway and has a 14.2 gallon tank.  How many freeway miles can you drive on a full tank of gas? You just bought a house and your mortgage payments are \$1004.23.  You will being making monthly payments for 30 years.  How much total money will you pay on this loan?      Back to the Decimals page Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions