Calculating Products of Decimals

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Student Summary

To multiply two decimals, such as (1.25)⋅(0.7)(1.25) \boldcdot (0.7), we can multiply the whole numbers that have the same digits, 125⋅7125 \boldcdot 7, and then use what we know about place value to place the decimal point.

  • Multiplying 125 and 7 gives 875.
  • We know that 125 is 100 times 1.25, and 7 is 10 times 0.7, so the product of 125 and 7 is 1,000 times the product of 1.25 and 0.7.
  • This means we need to divide 875 by 1,000, which moves the digits 3 places to the right and gives 0.875. 

Let’s find the product of 8.4 and 4.3!

  • First, we multiply 84 and 43. 
  • 84 is 10 times 8.4, and 43 is 10 times 4.3, so the product of 84 and 43 is 100 times the product of 8.4 and 4.3. 
  • Dividing 3,612 by 100 moves the digits 2 places to the right, giving 36.12. 

Notice that:

  • The factor 1.25 has 2 decimal places, the factor 0.7 has 1 decimal place, and the product 0.875 has 3 decimal places.
  • The factors 8.4 and 4.3 each have 1 decimal place, and the product 36.12 has 2 decimal places.

In general, to find the product of decimals, we can first multiply the corresponding whole numbers. Then we can place the decimal point so the product has as many decimal places as the sum of decimal places in the factors.

Visual / Anchor Chart

Standards

Building On
5.NBT.7

5.NBT.B.7

Addressing
6.NS.3

6.NS.B.3

Building Toward
6.EE.A

6.EE.A