EM3SRB_G5_54A-54J.qxd
11/3/08
2:28 PM
Page 99
Decimals and Percents
U.S. Traditional Long Division: Decimal Dividends
You can use U.S. traditional long division to divide money in
dollars-and-cents notation.
Share $8.17 among 5 people.
Step 1: Share the 8 dollars.
1
5$
8
.1
7
5
3
Ò Each person gets 1 dollar.
Ò 1 dollar each for 5 people
Ò 3 dollars are left.
Step 2: Trade the dollars for dimes. Share the dimes.
1. 6
5$
8
.1
7
5
31
3 0
1
Ò Each person gets 6 dimes. Write a decimal
point to show amounts less than a dollar.
Ò 30 dimes 1 dime
Ò 6 dimes each for 5 people
Ò 1 dime is left.
Step 3: Trade the dime for pennies. Share the pennies.
Ò Each person gets 3 pennies.
1.63
5$
8
.1
7
5
31
3 0
Ò 10 pennies 7 pennies
17
15
Ò 3 pennies each for 5 people
Ò 2 pennies are left.
2
Each person gets $1.63. There is 2¢ left.
$8.17 / 5 ∑ $1.63 R2¢
Divide.
1. $6.25 / 5 = ?
2. 5$
6
.7
5
3. 8$
4
.8
0
4. $3.85 / 7 = ?
Check your answers on page 442.
54E
EM3SRB_G5_54A-54J.qxd
11/5/08
11:00 AM
Page 100
Decimals and Percents
You can use U.S. traditional long division to divide decimals that
do not represent money.
2.79 / 6 = ?
Step 1: Trade the ones for tenths and share the tenths.
.4
62
.7
9
2 4
3
Ò
Ò
Ò
Ò
Each share gets 4 tenths. Write a decimal point in the quotient.
2 ones 7 tenths 27 tenths
4 tenths * 6 shares 24 tenths
3 tenths are left.
Step 2: Trade the remaining tenths for hundredths. Share the hundredths.
.46
62
.7
9
2 4
39
36
3
Ò Each share gets 6 hundredths.
Ò 3 tenths 9 hundredths 39 hundredths
Ò 6 hundredths * 6 shares 36 hundredths
Ò 3 hundredths are left.
At this point, you can either round 0.46 to 0.5 and write 2.79 / 6 0.5,
or you can continue dividing into the thousandths.
Step 3: Continue dividing into the thousandths. Add a 0 to the end of 2.79.
(Adding 0s or “padding” a decimal with 0s doesn’t change its value.)
.465
62
.7
9
0
2 4
39
36
30
30
0
Ò Each share gets 5 thousandths.
Ò 3 hundredths 0 thousandths 30 thousandths
Ò 5 thousandths * 6 shares 30 thousandths
Ò No thousandths are left.
2.79 / 6 0.465
Divide.
1. 6.29 / 4 = ?
2. 37
.8
3
3. 48
.3
7
Check your answers on page 442.
54F
4. 6.74 / 8 = ?
EM3SRB_G5_54A-54J.qxd
11/3/08
2:53 PM
Page 103
Decimals and Percents
U.S. Traditional Long Division:
Renaming Fractions as Decimals
Any whole number can
be written as a decimal
by attaching a decimal
point and one or more
0s; the value of the
number remains the
same: 5 5.0.
U.S. traditional long division can be used to rename
fractions as decimals.
With all decimal numbers,
attaching one or more
zeros to the right of the
digit that is furthest to the
right will not change the
value of the number:
8.3 8.3000.
5
Use U.S. traditional long division to rename 8 as a decimal.
Step 1: Write 58 as a division problem. Write 5 with several 0s after the
decimal point: 5.000. (You can always add more 0s if you need them.)
.0
0
85
0
Step 2: Solve the division problem. Stop when the remainder is 0, or when you have
enough precision for your purposes, or when you notice a repeating pattern.
.625
85
.0
0
0
4 8
20
16
40
40
0
This division problem divided evenly in three decimal places.
5
8
0.625
54I
EM3SRB_G5_54A-54J_CA.qxd
9/27/08
3:27 AM
Page 104
Decimals and Percents
Use U.S. traditional long division to rename
7
11
as a decimal.
Step 1: Write 171 as a division problem. Write 7 with several 0s after the
decimal point: 7.000. (You can always add more 0s if you need them.)
.0
0
117
0
Step 2: Solve the division problem. Stop when the remainder is 0, or when you have
enough precision for your purposes, or when you notice a repeating pattern.
.636363
117
.0
0
0
0
0
0
6 6
40
33
70
66
40
33
70
66
40
33
7
The digits 6 and 3 in the quotient appear to repeat forever.
7
11
0.636363... = 0.6
3
Use long division to rename these fractions as decimals.
5
1. 6
2.
2
11
5
3. 9
Check your answers on page 442.
54J
4. 7
3