# 12. Dividing Decimals by Decimals - Livingston Public .12. Dividing Decimals by Decimals ... //

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• 12.DividingDecimalsbyDecimals January06,2016

Warm Up 010616

Day 75th of school

1) 12.57 4

2) 0.91 7

3) 8.96 4

4) 6.67 3

5) 9 12

Dividing Decimals

Divide decimals

To divide a decimal by a whole number:Use long division.Bring the decimal point up in the answer

56.08

28 04

2

Yesterday we discussed... To divide a number by a decimal:

Change the divisor to a whole number by multiplying by a power of 10

Multiply the dividend by the same power of 10

Divide

Bring the decimal point up into the quotient

divisor ) dividend

• 12.DividingDecimalsbyDecimals January06,2016

15.6 6.24

Multiply the divisor 15.6 by 10, so that 15.6 becomes 156, and the dividend 6.24 must also be multiplied by 10 to become 624.

156 62.4

0.234 23.4

Multiply by 1000, so that the divisor 0.234 becomes 234, and the dividend 23.4 must also be multiplied by 1000 to become 23,400

234 23400

Try rewriting these problems so you are ready to divide!

Rewrite each problem after multiplying the divisor and dividend by a power of 10.

A)

B)

C)

D)

4.15 250

0.08

0.9

68.342

4.2

678.921

2.2

9 6789.21

22 683.42

8 420

250 4.15

Now do the division for the first two!

40201640400

25016501500150015000

Examples

A. B.

1 Divide

0.78 0.02

• 12.DividingDecimalsbyDecimals January06,2016

2

0.6 4.866

3

10 divided by 0.25

412.03 0.04

5

0.012 24.6

• 12.DividingDecimalsbyDecimals January06,2016

There are three types of decimals terminating, repeating, and nonterminating, nonrepeating .

A terminating decimal is a decimal that ends.All of the examples we have completed so far are terminating.

A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern.

A nonterminating, nonrepeating decimal neither repeats nor terminates. What "famous" decimal number do you know of that is this type?

To denote a repeating decimal, a line, called a vinculum, is drawn above the numbers that repeat, such as 15.32. However, calculators round the last digit and does not show repeating digits.

Let's consider the following...

l4Te

acher

Notes

• 12.DividingDecimalsbyDecimals January06,2016

29 311

31.0645

66232214213210088

120 110100 repeats

51.6

• 12.DividingDecimalsbyDecimals January06,2016

266.6

46.6

0.0077

19.133

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