Dividing by Decimals

3-6 Dividing by Decimals

Dividing by Decimals


Dividing by Decimals

Essential Question:

How do operations with decimals compare

to operations with whole numbers?


MA.6.A.1.3 Solve real-world problems involving…division of…decimals.

Also MA.6.A.1.1, MA.6.A.1.2. MA.6.A.5.3

Sunshine State Standards


Warm UpDivide.

1. 4.8 ÷ 2

2. 16.1 ÷ 7

3. 0.36 ÷ 3

4. 25.28 ÷ 4

2.42.3

0.12

6.32


Divisor

Quotient

Remember!

0.150.755

Dividend


What is a terminating decimal?

What is a repeating decimal?



A terminating decimal is one

that terminates or ends.







A repeating decimal is one

that keeps going and

repeats a pattern.





1 ÷ 8 = .125




repeats a pattern.





1 ÷ 8 = .125




repeats a pattern.

_

1 ÷ 3 = .3




Complete the table below:Whole Number

Powers of 10Decimal

Powers of 10

10 x 8.3 = 0.1 x 8.3 =

100 x 8.3 = 0.01 x 8.3 =

1,000 x 8.3 = 0.001 x 8.3 =

10,000 x 8.3 = 0.0001 x 8.3 =



Powers of 10Decimal

Powers of 10

10 x 8.3 = 83 0.1 x 8.3 =

100 x 8.3 = 830 0.01 x 8.3 =

1,000 x 8.3 = 8,300 0.001 x 8.3 =

10,000 x 8.3 = 83,000 0.0001 x 8.3 =



Powers of 10Decimal

Powers of 10

10 x 8.3 = 83 0.1 x 8.3 = 0.83

100 x 8.3 = 830 0.01 x 8.3 = 0.083

1,000 x 8.3 = 8,300 0.001 x 8.3 = 0.0083

10,000 x 8.3 = 83,000 0.0001 x 8.3 = 0.00083


What do you notice about the decimal point when you multiply by whole number powers of 10?

Of decimal powers of 10?


Multiplying by Powers of 10

Multiplying by whole number powers of 10:

• Move the decimal point one place to the right for each zero in the whole number power of 10.

• 3.995 x 100 = 3 9 9. 5

Multiplying by decimal powers of 10:

• Move the decimal point one place to the left for each decimal place in the decimal power of 10.

• 399.5 x 0.001 = 0.3 9 9 5


What do you think will happen to the decimal point when you divide by whole number powers of 10?

Of decimal powers of 10?


Dividing by Powers of 10

Dividing by whole number powers of 10:

• Move the decimal point one place to the left for each zero in the whole number power of 10.

• 35 ÷ 100 = 0 . 3 5

Dividing by decimal powers of 10:

• Move the decimal one place to the right for each decimal place in the decimal power of 10.

• 35 ÷ 0.001 = 3 5 0 0 0 .


Multiplying the divisor and the dividend by the same number does not change the quotient.

42 ÷ 6 = 7

10 10

420 ÷ 60 = 7

10 10

4,200 ÷ 600 = 7

Helpful Hint


Dividing a Decimal by a Decimal

Find the quotient.

5.2 ÷ 1.3

1.3 5.2 Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10.

Think: 1.3 x 10 = 13 5.2 x 10 = 52

Divide as with whole numbers. 13 52

4

–520

5.2 ÷ 1.3 = 4


Check It Out:

51.2 ÷ 0.24

0.24 51.2

Think: 0.24 x 100 = 24 51.2 x 100 = 5,120

Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.

24 5120.00

0


Check It Out:

Place the decimal point in the quotient. Divide as with whole numbers.

24 5,120.001

-48

2

32 -24

80-72

3

80

.3

-72

-72 80

3

51.2 ÷ 0.24 = 213.3__

When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

8


11 Understand the Problem

22 Make a Plan

Solve33

Look Back 44

Make a Problem Solving Plan:


Problem Solving Application

After driving 216.3 miles, the Yorks filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas?

11 Understand the Problem

The answer will be the average number of miles per gallon.

List the important information:

They drove 216.3 miles. They used 10.5 gallons of gas.


22 Make a Plan

Solve a simpler problem by replacing the decimals in the problem with whole numbers.

If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem.

Solve33

First estimate the answer. You can use compatible numbers.

216.3 ÷ 10.5 200 ÷ 10 = 20


The York family averaged 20.6 miles per gallon.

105 2163.0-210

2

63 -0630

-630

0

0

.6

Solve Continued33

10.5 216.3Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163

Place the decimal point in the quotient. Divide as with whole numbers.


Look Back44

The answer is reasonable since 20.6 is close to the estimate of 20.


John spent $13.44

renting 4 videos for

the weekend. What

was the cost per

video?


John spent $13.44

renting 4 videos for

the weekend. What

was the cost per

video?

$3.36

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Dividing by Decimals