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.
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