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Decimal Multiplication

Multiply decimals like whole numbers, then place the decimal point.

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Decimal Multiplication

Let’s Think About It

Micah is preparing to go on a climbing trip and needs to buy climbing rope. The cost of the rope is $1.59 per foot. He wants to buy 195.5 feet of rope. How much will the rope cost?

In this concept, you will learn how to multiply a decimal number with another decimal number.

Guidance

One way to multiply decimals is using area models. Another more efficient way to multiply two decimals is to ignore the decimal and multiply the numbers as if they were whole numbers first. Afterwards, add the decimal point back into the product. It is important to place the decimal point in the correct place.

Here is another multiplication problem.

4.7×2.1=

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

4.7×2.1 47+940   987
  

Then, place the decimal point into the product. Count the number of decimal places both multipliers. 4.7 has 1 decimal place. 2.1 also has 1 decimal places. There are a total of 2 decimal places. Move the decimal point 2 places to the left. Remember that the decimal point is located to the right of the ones place in a whole number.
If you need to move the decimal point more places than there are digits, you can always use zero placeholders.

9.87

The product of 4.7 times 2.1 is 9.87.

Check to see if the decimal point was placed correctly by estimating the product of 4.7 times 2.1.

First, round the decimal numbers to the nearest whole number.

4.7 rounds to 5.

2.1 rounds to 2.

Then, multiply to find an estimate product.

5×2=10

Next, compare the products. The actual product should be close to the estimate product. 9.87 is close to 10. The decimal point was placed in the right location.

Guided Practice

Multiply the decimals.

0.134×0.567=

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

    0.134×0.567   938     804+670   75978

Then, place the decimal point into the product. Count the number of decimal places both multipliers. 0.134 has 3 decimal places. 0.567 also has 3 decimal places. There are a total of 6 decimal places. Move the decimal point 6 places to the left. Remember that the decimal point is located to the right of the ones place in a whole number. Use a zero placeholder if needed.

0.075978
 

The product of 0.134 times 0.567 is 0.075978

Examples

Multiply the decimals.

Example 1

3.1×4.9=

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

  3.1 ×4.9 279+124   1519

Then, place the decimal point into the product. There are a total of 2 decimal places in the multiplicands. Move the decimal point 2 places to the left.

15.19

The product of 3.1 times 4.9 is 15.19.

Example 2

1.2×5.1=

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

1.2×5.1 12+60   612
 

Then, place the decimal point into the product. There are a total of 2 decimal places in the multiplicands. Move the decimal point 2 places to the left.

6.12

The product of 1.2 times 5.1 is 6.12.

Example 3

3.21×6.7=
 

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

  3.21  ×6.7 2247+1926   21507
 

Then, place the decimal point into the product. There are a total of 3 decimal places in the multiplicands. Move the decimal point 3 places to the left.

21.507

The product of 3.21 times 6.7 is 21.507.

Follow Up

Remember Micah on the climbing trip?

Micah wants to buy 195.5 feet of rope that costs $1.59 per foot. Multiply 195.5 by $1.59 to find the total cost of the rope.

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

      195.5    ×1.59     17595     9775+1995   310845
  

Then, place the decimal point into the product. There are a total of 3 decimal places in the multiplicands. Move the decimal point 3 places to the left.

310.845
 

The cost of the rope should be $310.845, but remember that dollars are only calculated to the hundredths place. Round the decimal to the nearest hundredths place.

310.845310.85

Micah will spend $310.85 on climbing rope.

Video Review

https://www.youtube.com/watch?feature=player_embedded&v=Zt_rFDQCi2I

https://www.youtube.com/watch?v=55OtS_Dil1Y

Explore More

Multiply the following decimals.

  1. 4.3×0.12=
  2. 2.3×3.4=
  3. 0.34×0.56=
  4. 2.7×3.2=
  5. 6.5×2.7=
  6. 0.23×0.56=
  7. 1.23×0.4=
  8. 0.5×0.76=
  9. 0.23×0.8=
  10. 3.45×1.23=
  11. 1.45×0.23=
  12. 0.89×0.9=
  13. 0.245×0.8= 
  14. 34.5×0.7=
  15. 18.7×0.9=
  16. 22.3×0.76=
  17. 21.7×0.4=.
  18. 14.5×0.68=
  19. 20.1×0.3= 
  20. 34.23×0.18=
  21. 0.189×0.9= 
  22. 0.341×0.123=
  23. 0.451×0.12=
  24. 0.768×0.123=
  25. 0.76×0.899=

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 4.9. 

Vocabulary

Horizontally

Horizontally

Horizontally means written across in rows.
Hundreds grid

Hundreds grid

A hundreds grid is a grid of one hundred boxes used to show hundredths when working with decimals.
Product

Product

The product is the result after two amounts have been multiplied.
Vertically

Vertically

Vertically means written up and down in columns.

Image Attributions

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