Math 40
Prealgebra
Section 5.4 – Dividing Decimals
5.4 Dividing Decimals
Review from Section 1.3:
Quotients, Dividends, and Divisors.
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 In the expression, 4 12 , the number 12 is called the dividend, 4 is called the divisor, and 3 is
called the quotient.

12  4  3
is equivalent to
3
4 12
is equivalent to
12
 3 is equivalent to divide 12 by 4
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Steps for Dividing Decimal Numbers
1. The divisor (the outside number) needs to be a whole number. If the divisor contains a decimal
you will need to move the decimal point to the end of the divisor.
i. Count the number of times you will need to move the decimal point so that it is at the end of
the divisor.
ii. You will need to move the decimal point of the dividend (the inside number) the exact same
number of times.
2. Perform the division as if the numbers were whole numbers.

You may need to add zeros to the back of the dividend to complete the division
3. Place the decimal point in the quotient immediately above the decimal point in the dividend.
(Carry the decimal point up.)
Example 1: Divide 23 by 20.
Solution:
20 23
1
20 23
20
3
1.15
20 23.00
Since we are in the decimal chapter, we will not stop when we have a remainder.
Instead we will add a decimal point and a zero to the back of the dividend. We will
continue to divide and add zeros to the back of the dividend until we get a remainder
of zero or the problem tells us to round to a specific decimal place.
Don’t forget to carry the decimal point up into the quotient.
20
30
Hence, 20 23  1.15 .
2 0
1 00
1 0 0
0
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2015 Worrel
Math 40
Prealgebra
Section 5.4 – Dividing Decimals
You Try It 1: Divide 34 by 25.
Example 2: Divide. 155.2  25
Solution:
25 155.2
6.208
25 155.200
Don’t forget to carry the decimal point up into the quotient.
150
52
5 0
Hence, 155.2  25  6.208 .
20
0
200
2 0 0
0
You Try It 2: Divide. 42.55  23
Example 3: Divide. 0.36 4.392
Solution:
0.36 4.392
0.36. 4.39.2
12.2
36 439.2
Since we have a decimal point in the divisor, we will need to move the
decimal point to the end. In this case the decimal point needs to move
TWO times to move to the end. This means we will need to move the
decimal point in the dividend, TWO times to the right as well.
becomes
36 439.2
Don’t forget to carry the decimal point up into the quotient.
36
79
Hence, 0.36 4.392  12.2 .
72
72
7 2
0
You Try It 3: Divide. 0.45 36.99
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2015 Worrel
Math 40
Prealgebra
Section 5.4 – Dividing Decimals
Review of Dividing Signed Numbers
Like Signs: The quotient to two numbers with like signs is positive.
  
  


Unlike Signs: The quotient to two numbers with unlike signs is negative.
  
  


Example 4: Divide. 0.03  0.024
Solution: Since we have unlike signs, we know that our answer should be negative.
0.024 0.03 Since we have a decimal point in the divisor, we will need to move the
decimal point to the end. In this case the decimal point needs to move
THREE times to move to the end. This means we will need to move
the decimal point in the dividend, THREE times to the right as well.
0.024. 0.030.
1.25
24 30.00
becomes
24 30
We will need to add a decimal point and zeros behind the 30 to complete the division.
Don’t forget to carry the decimal point up into the quotient.
24
60
Hence, 0.03  0.024  1.25 .
4 8
12 0
Don’t forget to put the negative sign in your answer!
1 2 0
0
You Try It 4: Divide. 0.0113  0.05
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2015 Worrel
Math 40
Prealgebra
Section 5.4 – Dividing Decimals
Example 5: Convert
Solution: 7 4
7 4.000
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to a decimal. Round your answer to the nearest hundredth.
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We will add a decimal point to the back of the dividend, 4, and add zeros behind
the decimal point as needed.
Since the directions ask us to round, we do not need to keep dividing until we get no remainder.
Instead, we will divide to one place value past where the problem is asking us to round.
For example, this question asks us to round to the nearest hundredth. Therefore we must divide until
we have a thousandths place (one place value past a hundredth). The reason we need one more place
value past what is asked is because we need a testing digit to be able to see how to round the
rounding digit. (See Section 1.1 for a review on rounding.)
0.571
Don’t forget to carry the decimal point up into the quotient.
7 4.000
3 5
50
4 9
So we have
4
 0 . 5 7 1  0.57
7
10
7
rounding digit
testing digit
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You Try It 5: Convert
5
to a decimal. Round your answer to the nearest hundredth.
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Dividing by Powers of Ten
Consider:
123.4567  101  12.34567
123.4567  10 2  1.234567
123.4567  103  0.1234567
123.4567  10 4  0.01234567
Dividing by Powers of Ten
Dividing a number by 10n will move the decimal point n places to the left.
EX: 23.58941 104  0.0023.58941  0.002358941
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2015 Worrel
Math 40
Prealgebra
Section 5.4 – Dividing Decimals
Example 6: Simplify. 123456.7 104
Solution: According to the Dividing by Powers of Ten rule, dividing by 104 should move the decimal
point FOUR places to the left.
123456.7 104  12.3456.7  12.34567
You Try It 6: Simplify. 123456.7 102
Note:
Multiplying and Dividing by Powers of Ten have very similar steps. The only difference is for
one you move RIGHT and for the other you move LEFT.
Multiplying by Powers of Ten
 Multiplying a number by 10n will move the decimal point n places to the RIGHT.
 When multiplying by 10n , your answer will be larger than the dividend. This is why the
decimal is moving to the RIGHT.
Dividing by Powers of Ten
 Dividing a number by 10n will move the decimal point n places to the LEFT.
 When dividing by 10n , your answer will be smaller than the dividend. This is why the
decimal is moving to the LEFT.
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2015 Worrel