Lesson 6
Dividing Decimals

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Review the names of the parts of a division operation.

The procedures for dividing decimal values is virtually identical to the work you have already mastered with dividing whole numbers and integers. The big difference here is the need to deal with placing the decimal point in the quotient.

Topic 1
Placing the Decimal Point: Divisor is a Whole Number

Procedure

When the divisor is a whole number

The decimal point in the quotient for division problems is always located directly over the decimal point in the divisor.

This applies only when the divisor is a whole-number value.

Examples

     6.1
5 )30.5 		     42.5
9 )382.5 		       18.02
25 )450.5

 3.105
350 )1086.720    
(rounded to the nearest thousandth)

Exercises

Rewrite the solution to the given division problems, showing the location of the decimal point.

Topic 2
Placing the Decimal Point -- Divisor Has a Decimal Part

Here is a multiplication problem where the dividend has no decimal part. In the previous topic in this lesson, you know you proceed with the division operations, irrespective of the decimal points, then place the decimal point in your answer directly over the one in the dividend. Simple.

       18.02
25 )450.5

But what if the divisor in this example is changed to 2.5? The quotient will actually have the number combination 1802 , but where does the decimal point go?

2.5 )450.5

The "secret" to dividing by a decimal  value is straightforward: Convert the divisor to a whole-number value and then divide.

And exactly how do you go about doing that? In this example, multiplying the divisor by a factor of 10 eliminates the decimal part:

2.5 x 10 = 25

But you know it is essential to keep the numbers balanced in such problems, so in this instance you also have to multiply the divident by a factor of 10:

450.5 x 10 = 4505

Now the original problem looks like this:

25 )4505

You know what do to from here:

       180.2
25 )4505

Procedure

When the divisor is has a decimal part

  1. Multiply the divisor by factors of 10 until the decimal part is gone.
  2. Multiply the dividend by the same factors of 10
  3. Complete the division as with problems where the divisor has no decimal part.

The decimal point in the quotient is then located directly over the decimal point in the divisor.

Exercises

Prepare these problems for division by converting the divisor to a whole-number value.

If you are having any trouble understanding the content of this lesson, you will benefit from a more detailed tutorial on the subject.