Division of Decimals        Dividing a Decimal by a Whole Number Dividing a decimal by a whole number is similar to dividing whole numbers.  One must only be sure to line up the decimal point of the dividend with that of the quotient.   Example Divide     143.22 ÷ 6 Solution                23.87         6 | 143.22                12        Hence  143.22 ÷ 6  =  23.87 Example Divide     41.472 ÷ 12 Solution                .456         12 | .472                  36      Hence  41.472 ÷ 12   =  3.456 Exercises Divide 0.4544 ÷ 8    0.0357 ÷ 17      Dividing and Rounding Decimals Typically division problems yield remainders.  When this is the case we usually do not write the quotient as a mix of decimal and fraction but rather round to an indicated decimal place.  Since rounding involves looking at the digit to the right, we need to find this digit when we do this division.  If necessary, we pad the number with zeros to the right. Example Divide and round to the nearest hundredth.         3.64 ÷ 7 Solution Since we need to round to the nearest hundredth, we will need to see the thousandths digit.  We rewrite         3.650 ÷ 7              0.521         7 | 3.650                35                        15                       14                     10                     7                    END HERE Since  1 < 5 we do not round up, hence our answer is 0.52 Exercise Divide  52.37 ÷ 11  and round to the nearest thousandth. Dividing a Decimal by a Decimal Yes Tashia, we finally get to move the decimals around.   To divide a decimal by a decimal, we move each decimal point to the right until the divisor becomes a whole number.  We may need to pad the dividend with extra zeros first. Example Divide  6.693 ÷ 0.3   Solution Since the divisor 0.3 has one digit to the right of the decimal we move both decimals one place to the right         66.93 ÷ 3   Now the divisor is a whole number.  We divide              22.31         3 | 66.93                6                     06                        6                     09                       9                        03                       3                       0 Exercises Divide 17.25 ÷ 2.3    0.00102 ÷ 5.1    0.000253 ÷ 0.0011           Applications Example You have driven 99.2 miles on your recent trip to Sacramento.  If your car used 7.1 gallons, what was your gas mileage?  Round your answer to the nearest tenth. Solution  This is a division problem since dividing miles by gallons gives miles per gallon.                  13.97         71 | 992.00                  71                      282                       213                     690                     639                        510                    END Now round to the nearest tenth.  Your car got 14.0 miles to the gallon.                     Example  You are planning an event that will cost a total of \$206.15 for 34 attendees.  What is the cost per attendee? Solution This is a division problem                    6.063         34 | 206.150                  204                          215                           204                          110                            END              Now round to the nearest penny.  The cost per person is \$6.06.   Back to the Decimals page Back to the Math 187A page e-mail Questions and Suggestions