Arithmetic Grade Five

Lesson Fifty-one: Decimal Multiplication

Take a look at this bunch of decimal multiplication problems: 

  .07 x .7 = .049		.07 x .07 = .0049

  .8 x .06 = .048		.08 x .06 = .0048

  .5 x .03 = .015		.05 x .03 = .0015
If you study these problems carefully you will notice that the number of decimal places in the problem is equal to the number of decimal places in the answer. 

  .07 x .07     	Both .07 and .07 have two decimal places for
			a total of four decimal places.

  7 x 7 = 49		Multiplying 7 x 7 = 49

  .0049			Placing a decimal and two zeroes in front of
			the 49 gives us an answer with four decimal places
Here's another example: 

  .6 x .09     		.6 has one decimal place and .09 has two 
			decimal places for a total of three decimal
			places.

  6 x 9 = 54		Multiplying 6 x 9 = 54

  .054			Placing a decimal and one zero in front of the
			54 gives us an answer with three decimal places
Here's another example: 

  .01 x .01     	.1 has two decimal places and .01 has two 
			decimal places for a total of four decimal
			places.

  1 x 1 = 1		Multiplying 1 x 1 = 1

  .0001			Placing a decimal and three zeroes in front of 
			the 1 gives us an answer with four decimal places
Tricky situation: 

  .05 x .04		Four decimal places in problem

  5 x 4 = 20		Simple multiplication

  .0020			Placement of zeroes and decimal place to create
			correct answer

  .002			Drop the trailing zero to create preferred format

In this last case we wind up with an answer with only three decimal places even though there are four decimal places in the problem because we drop the optional trailing zero.

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