1

Multiplying Decimals by Decimals

2

DecimalDecimalReviewReview

3

Decimals Represent Fractions

6 . 8 3 6 1

Ten

ths

Hun

dred

ths

Tho

usan

dths

6 8/10 3/100 6/1000 1/10,000

Notice that every decimal ends with “ths”.

One

s

Ten

thou

sand

ths

4

Which decimal place value is missing?

Ten ThousandthsO

nes

Ten

ths

Hun

dred

ths

6 . 8 3 6 2

Ten

Tho

usan

dths

Tho

usan

dths

5

Which decimal place value is missing?

ThousandthsO

nes

Ten

ths

Hun

dred

ths

6 . 8 3 6 2

Ten

Tho

usan

dths

Tho

usan

dths

6

Which decimal place value is missing?

TenthsO

nes

Ten

ths

Hun

dred

ths

6 . 8 3 6 2

Ten

Tho

usan

dths

Tho

usan

dths

7

Which decimal place value is missing?

HundredthsO

nes

Ten

ths

Hun

dred

ths

6 . 8 3 6 2

Ten

Tho

usan

dths

Tho

usan

dths

8

How to How to MultiplyMultiply

DecimalsDecimals

9

3.15 x 1.9 3.15 x 1.9 Round to the nearest whole number to estimate answerRound to the nearest whole number to estimate answer

3 x 2 3 x 2

= 6 = 6 Do the multiplication (just ignore the decimals for now)Do the multiplication (just ignore the decimals for now)

315315 x 19 x 19 5 5

4 4

3 3

1 1

28 28 5 5

0 0

1 1

3 3 5 5

8 8

9 9

5 5

So our answer should So our answer should be somewhere around 6be somewhere around 6

10

Our estimate Our estimate

5 9 8 55 9 8 5

Based on our estimate, where do

Based on our estimate, where do

you think the decimal should go?

you think the decimal should go?

Answer before doing Answer before doing

anything with decimalsanything with decimals

6 6 . .

Let’s look at another example to Let’s look at another example to see if we can come up with a see if we can come up with a

rule…..rule…..

11

2.7 x 1.1 2.7 x 1.1 Round to the nearest whole number to estimate answerRound to the nearest whole number to estimate answer

3 x 1 3 x 1

= 3 = 3 Do the multiplication (just ignore the decimals for now)Do the multiplication (just ignore the decimals for now)

2727 x 11 x 11 7 7

2 2 7 7

0 0

2 2 7 7

9 9

2 2

So our answer should So our answer should be somewhere around 3be somewhere around 3

12

Our estimate Our estimate

2 9 7 2 9 7

Based on our estimate, where do

Based on our estimate, where do

you think the decimal should go?

you think the decimal should go?

Answer before doing Answer before doing

anything with decimalsanything with decimals

3 3 . .

One more example…..One more example…..

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4.125 x 1.8 4.125 x 1.8 Round to the nearest whole number to estimate answerRound to the nearest whole number to estimate answer

4 x 2 4 x 2 = 8 = 8 Do the multiplication (just ignore the decimals for now)Do the multiplication (just ignore the decimals for now)

41254125 x 18 x 18

0 0

4 4

0 0

2 2

0 0 5 5

0 0

2 2

1 1 0 0

5 5

2 2

4 4

So our answer should be So our answer should be somewhere around 8somewhere around 8

1 1

33 33 4 4 7 7

14

Our estimate Our estimate

7 4 2 5 0 7 4 2 5 0

Based on our estimate, where do

Based on our estimate, where do

you think the decimal should go?

you think the decimal should go?

Answer before doing Answer before doing

anything with decimalsanything with decimals

8 8 . .

Ok, lets look at all of our Ok, lets look at all of our examples…..examples…..

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ProblemProblem

7.4250 7.4250

Number of Number of Decimal Decimal Places in Places in problemproblem AnswerAnswer

4.125 x 1.84.125 x 1.8

2.7 x 1.12.7 x 1.1

3.15 x 1.93.15 x 1.9

2.97 2.97

5.985 5.985

Number of Number of Decimal Decimal Places in Places in answeranswer

33 33

22

44

22

44

Look at the number of places after the Look at the number of places after the decimal point in both the problem and the decimal point in both the problem and the answer……answer……

Copyright © 2013 by Monica Yuskaitis16

x4.235

61. x4.235

67 6230

1. 4.235 1.8x

How to multiply decimals

Estimatethe

productsfirst.

Count the # of digitsin decimal places in

the factors. That’s thenumber of decimal

places in the product.

1 2 3

Multiply (ignore

decimal)

4

2 8 76230

123

4

.1234

17

Solve this problem

9. 8 7. 4x

8

2

4

3

3 9.

18

Solve this problem

5. 2 3. 2 1x

3256 x41 0 +

3890.1

19

Solve this problem

7 6. 84. 3 5x

0

4

4

3

3 84 x

2

0

2

2 3x x273 0

32

+080

1

4

1

33 .

20

ProblemProblemSolvingSolving

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George lived 13.7 miles from his school. He walked 1/2 (.5) of the way. How far did he walk?

13.7 miles

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.5 of 13.7• The first thing to remember is “of”

means multiply in mathematics.

of = x

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.5 x 13.7

1 3.7.x5

3

8

1

6 .

5

miles