Dividing Decimals

Lesson 1-3

Remember the parts of a division problem:

5

45

9

dividend

divisor

quotient

Dividing a Decimal by a Whole Number

• Place the decimal point in the quotient directly above the decimal point in the dividend.
• Divide as you normally would (DMSCB)

Example

5

12.5

.

DMSCB

2

10

2

5

5

25

0

Example 2

9

101.52

.

1

9

1

1

1

9

2

5

2

18

7

2

8

72

0

Dividing a Decimal by a Decimal

• Move the decimal point in the divisor to the right, until you get to the end of the digits.
• Count how many places you moved that decimal.
• Move the decimal point in the dividend the same number of places to the right that you moved the decimal point in the divisor.

Example

0.3

6.72

one space

03

67.2

New problem

3

67.2

DMSCB

.

2

6

0

7

2

6

1

2

4

1 2

0

Example 2

3.2

2.24

32

22.4

.

32

x 5

160

32

x 8

256

32

x 7

224

7

22 4

0

Example 3

0.38

13.3

The decimal must be moved 2 spaces to the right.

When we move this one 2 spaces, we find that we need to add a space. What will we fill it with?

Answer: Fill it in with a 0. 13.3 becomes 1330

SO, our problem becomes 038 into 1330. 038 is the same as 38.

38

1330

38

x 5

190

38

x 4

152

38

x 3

114

3

114

19

0

5

190

0

Example 4

2.48

1.3392

248

133.92

248

133.92

.

248

x 5

1240

248

x 6

1488

5

124 0

9

9

2

248

x 4

992

4

9 92

0

Terminating and Repeating Decimals

• A terminating decimal is a decimal that stops, or terminates.
• Examples: 1.25 or 0.892
• A repeating decimal is a decimal that has a repeating digit or a repeating group of digits.
• Examples: 1.3333… or .121212121…
• Repeating decimals usually have a bar across the repeating portion.

2.3

62

8

7

56

6

.0

.

0

7

56

4

0

0

5

40

0

Terminating decimal

5

6

.0

.

8

4 8

2

0

0

3

18

2

0

0

3

18

2

This is a repeating decimal.

.83

Time For Homework!