Multiplying decimals by powers of 10

Lessons

In this lesson, we will learn:

• What are powers of 10?
• How to move the decimal place when multiplying decimals by powers of 10
• How to understand decimal multiplication using base ten (block) models

Notes:

• All place values are related to their neighboring place values by a factor of 10. A place value is 10 times more than the place to its right and 10 times less than the place to its left.


• Each place value can be represented as a power of ten

• Recall: repeated addition becomes multiplication, ex. 10 + 10 + 10 = 3 ×10
• Repeated multiplication becomes powers (or exponents), ex. 10×10×10 = 10³
• You can see that the exponent is the same as the number of zeroes represented

• What happens when you multiply by powers of ten?
• When you multiply any number by 1, it stays exactly the same!
• What happens when you multiply by 10? 100? 1000?

• You can use the number of zeroes as the number of places that a decimal must jump to the right when multiplying by powers of ten.
• If you run out of numbers when moving the decimal to the right, fill those spaces with trailing zeroes!


• We can also use base ten (block) models to multiply decimals with powers of 10. There are two different models, depending on what represents one whole:
• If one whole is represented by a hundred block (square): ex. multiplying 5 tens blocks by 10 will give you 5 wholes.

× 10 = 50 tens = 5 wholes =
• If one whole is represented by a thousand cube: ex. multiplying 3 ones blocks by 100 will give you 3/10 wholes (or 3 tenths).

$\large\square \, \square \,\square \,$ × 100 = 3 hundreds = 3/10 wholes =

• Introduction
  Introduction to multiplying decimals by powers of 10:
  a)

  What are powers of 10?
  
  
  b)

  What patterns can we see when using powers of 10 to multiply decimals?
  
  
  c)

  How can we use base ten (block) models to show decimal multiplication with powers of 10?
  
  

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• 1.
  Multiplying decimals by powers of 10 by moving the decimal
  Multiply:
  a)

  2.993 × 10 =?
  
  
  b)

  100 × 0.05 =?
  
  
  c)

  2.8 × 1000 =?
  
  

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• 2.
  Multiplying decimals by powers of 10 by filling in the blanks
  Fill in the missing number in the following questions:
  a)

  _____ × 0.408 = 408
  
  
  b)

  _____ × 10 = 93.25
  
  
  c)

  0.017 × _____ = 0.17
  
  
  d)

  1000 × _____ = 4280
  
  
  e)

  _____ × 0.56 = 56
  
  
  f)

  _____ × 100 = 6.1
  
  

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• 3.
  Using HUNDREDTHS block models for decimal multiplication by powers of 10
  If one whole is represented by a hundred block (big square made out of 100 tiny squares), then a tenth is represented by a stick (of 10 tiny squares). 10 tenths will make one whole, and 100 hundredths will make one whole.
  
  Show the following multiplication statements using base ten block models, and solve:
  a)

  0.7 × 10 =?
  
  
  b)

  0.32 × 100 =?
  
  

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• 4.
  Using THOUSANDTHS block models for decimal multiplication by powers of 10
  If one whole is represented by a thousand cube (cube made out of 10 hundred blocks/plates; 1000 tiny squares), then a tenth is represented by a hundred block (plate of 100 tiny squares). 10 hundred blocks will make one whole, and 1000 thousandths will make one whole.
  
  Show the following multiplication statements using base ten block models, and solve:
  a)

  0.004 × 1000 =?
  
  
  b)

  0.158 × 100 =?
  
  

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• 5.
  Word problem for decimal multiplication by powers of 10
  If the price of reusable metal drinking straws is $0.29 each when buying them straight from the factory, how much would it cost to buy 1000 metal straws in bulk?
  
  Write out the multiplication statement and solve.

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