Division of Decimals

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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
1. 0.4544 ÷ 8
2. 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
1. 17.25 ÷ 2.3
2. 0.00102 ÷ 5.1
3. 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.

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