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Multiplying Decimals including Powers of 10. NOTES: Multiplying Decimals. Line up numbers on the Right Side **Note: Multiplication is the ONLY operation where you don’t line up the decimals!!! Multiply and ignore the decimals Count the # of digits behind a decimal in the problem

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slide2

NOTES:Multiplying Decimals

  • Line up numbers on the Right Side

**Note: Multiplication is the ONLY operation where you don’t line up the decimals!!!

  • Multiply and ignore the decimals
  • Count the # of digits behind a decimal in the problem
  • Put the decimal in front of that many digitsin the product.
slide3

EXAMPLES:Multiplying Decimals

1) 1.82 x 3

1.82

x 3

There are 2 places behind the decimal!!!

5 4 6

slide4

EXAMPLES:Multiplying Decimals

2) (1.324)(6)

1.324

x 6

There are 3 places behind the decimal!!!

7 9 4 4

slide5

EXAMPLES:Multiplying Decimals

3) 0.9 · 0.8

0.9

x 0.8

There are 2 places behind the decimal!!!

7 2

slide6

EXAMPLES:Multiplying Decimals

4) 4.07 · 3.1

4.07

x 3.1

There are 3 places behind the decimal!!!

4 0 7

1 2 2 1 0

1 2 6 1 7

slide7

EXAMPLES:Multiplying Decimals

5) Write the multiplication expression for the picture:

0.6

0.6 x 1.6

1.6

slide8

1) What expression does the decimal model represent?

  • 0.3x1.4
  • 0.4x1.3
  • 1.3x0.5
  • 3x14
  • What is the answer? (Do the math!)
  • 0.3 x 1.4 = 0.42
slide9

NOTES:Evaluate Reasonableness

Tell whether each statement is sometimes, always, or never true. Give an example or counterexample for each.

When two numbers, both less than 1, are multiplied, the product is less than 1.

When two numbers, both greater than 1, are multiplied, the product is less than either factor.

Always; 0.5 x 0.6 = 0.3

Never; 1.5 x 2.3 = 3.45, and 3.45 > 1.5 and 2.3

slide10

NOTES:Evaluate Reasonableness

Tell whether each statement is sometimes, always, or never true. Give an example or counterexample for each.

When a number is multiplied with another number less than 1, the product is larger than the first value.

When a number is multiplied with a decimal greater than 1, the product is larger than the initial value.

Never; 16 x 0.5 = 8, and 8 < 16

Always; 16 x 1.5 = 24, and 24 > 16

slide11

NOTES:Multiply powers of 10

  • If Greater than 1:
  • Count the number of 0’s
  • Move the decimal to make the number bigger by that number of places!
  • If Less than 1:
  • Count the number of places after the decimal
  • Move the decimal to make the number smaller by that number of places!

0.35 x 100

=35

3.2 x .01

=0.032

slide12

EXAMPLES:Powers of 10

8500

1) 8.5 x 1000 =

2) 5.98 x 10,000 =

3) 93.6 x .1 =

4) 7.84 x .001 =

5) 2.72 x 100=

59,800

9.36

0.00784

272

slide13

EXAMPLES:Powers of 10

  • There are about 3.9 million miles of roads in the United States. Write the amount of roads in standard form.

There are 730 students enrolled at Curtis Middle School. Next year, enrollment is expected to increase by 1/10. By how many students will enrollment increase??

$3,900,000

730 x .1=

73

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