Decimal Division

Types of Decimal Division

1) Traditional2) Partial Quotients3) Fractional Notation

Example 1: Traditional

• 2.07 ÷ 0.003

• The first decimal goes “in the house” (Dividend is the Den)

• The second decimal goes in front of the house

2.070.003

Example 1: Traditional

Move the decimal point of each decimal until the divisor is a whole number, adding zeros to dividend if necessary

Estimate 2100 ÷ 3 = 700 Since all decimal points are at the end of the numbers,

divide normally – see next slide

2.070.003

2.07 3 00.00 ..

Example 1: Traditional/Partial Quotients

2070 3 2070 36

-18 27

9

-27 00

0

00 0

600-1800 270-270 0

90____ 690

Both methods show an answer close to our estimate of 700

Example 2: Traditional & Partial Quotients

Let’s try an example where a decimal point remains in the dividend (Den)

• 2.07 ÷ 0.3

• More decimal in divisor and dividend over 1 place.

• Estimate: 21 ÷ 3 = 7

2.07 0.3

20.7 3

Example 2: Traditional

20.7 3. 1. Put decimal point

directly above theone in the Den.

2.Does 3 go into 2? No.

3.Does 3 go into 20?Yes.

0

-18 2

6

7

4.Does 3 go into 27?Yes.

-27 0

9

6.9 is close to our estimate of 7

Example 2: Partial Quotients

20.7 31. Forget about decimal until the end.

3. Divide with benchmarks 3 x 50 = 150

5 0

3 x 10 = 30

-150 57 1 0

-30 27

3 x 9 = 27 9

-27 0

6 9

4. Since our estimate was 7, place decimal point between the 6 and the 9

Answer: 6.9

2. Estimate: 21 ÷ 3 = 7

Example:

• Let’s try: 0.125 ÷ 0.05

• Move decimal point so that the divisor (0.05) is a whole number

• Estimate: 10 ÷ 5 = 2

• Try your method

5 12.5

– What to do if there is a number leftover?

6.7 ÷ 0.21. Start the same…house/move decimal

points/make estimate

6.7 0.2

67 2 Estimate: 70/2 = 35

67 2 67 2

-6

-6 0

3

7

3

10

5

-10 0

03 0

-60 7 3

-6 1

0

0 5

-10 0

3 3 5

Estimate: 35Where does the decimal go?