Transcript 5.4:Dividing Decimals

5.4
Dividing Decimals
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Dividing by a Decimal
Division of decimal numbers is similar to division of
whole numbers.
The only difference is the placement of a decimal point in the
quotient.
If the divisor is a whole number, divide as for whole numbers; then
place the decimal point in the quotient directly above the decimal
point in the dividend.
0 84
divisor
63 52.92
- 504
2 52
-252
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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Martin-Gay, Prealgebra, 6ed
quotient
dividend
2
Dividing by a Decimal
If the divisor is not a whole number, we need to move the
decimal point to the right until the divisor is a whole
number before we divide.
divisor
6 . 3 52 . 92
dividend
63 . 529 . 2
84
63 52 9.2
- 504
25 2
-252
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Martin-Gay, Prealgebra, 6ed
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Dividing by a Decimal
Step 1: Move the decimal point in the divisor to the
right until the divisor is a whole number.
Step 2: Move the decimal point in the dividend to
the right the same number of places as the
decimal point was moved in Step 1.
Step 3: Divide. Place the decimal point in the
quotient directly over the moved decimal
point in the dividend.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
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Estimating When Dividing Decimals
Divide 258.3 ÷ 2.8
Exact
92.25
28. 2583.
- 252
63
- 56
70
- 56
140
- 140
0
Estimate
rounds to
100
3 300
This is a reasonable answer.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
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Dividing Decimals by Powers of 10
There are patterns that occur when dividing by powers
of 10, such as 10, 100, 1000, and so on.
456.2
= 45 . 62
10
The decimal point moved 1 place
to the left.
1 zero
456.2
= 0 . 4562
1 , 000
The decimal point moved 3 places
to the left.
3 zeros
The pattern suggests the following rule.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
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Dividing Decimals by Powers of 10
Move the decimal point of the dividend to the left the
same number of places as there are zeros in the power
of 10.
Notice that this is the same pattern as multiplying by powers of
10 such as 0.1, 0.01, or 0.001. Because dividing by a power of
1 ,
10 such as 100 is the same as multiplying by its reciprocal 100
or 0.01.
463.7
1
= 463.7 
= 463.7  0.01 = 4.637
100
100
To divide by a number is the same as multiplying by its reciprocal.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
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