Dividing DecimalsDividing Decimals

Section 5.4

The only difference is the placement of a decimal The only difference is the placement of a decimal point in the point in the quotientquotient. .

If the divisor is a whole number, divide as for If the divisor is a whole number, divide as for whole numbers; then place the decimal point in whole numbers; then place the decimal point in the quotient directly above the decimal point in the quotient directly above the decimal point in the dividend. the dividend. 8

- 5 0 42 52-2 52

0

divisor

quotient

dividend0 4

Division of decimal numbers is similar to Division of decimal numbers is similar to division of whole numbers. division of whole numbers.

63 52.92

2

863 529.2

- 504252-252

0

4

If the divisor is If the divisor is notnot a whole number, we need to move a whole number, we need to move the decimal point to the right until the divisor is a the decimal point to the right until the divisor is a whole number before we divide. whole number before we divide.

divisor dividend6 3 52 92. .

63 529 2. .

3Martin-Gay, Prealgebra, 5ed

Dividing by a DecimalDividing by a Decimal

Step 1. Move the decimal point in the divisor Step 1. Move the decimal point in the divisor to the right until the divisor is a whole to the right until the divisor is a whole number.number.

Step 2. Move the decimal point in the Step 2. Move the decimal point in the dividend to the right the dividend to the right the same same numbernumber ofof placesplaces as the decimal as the decimal point was moved in Step 1.point was moved in Step 1.

Step 3. Divide. Place the decimal point in the Step 3. Divide. Place the decimal point in the quotient directly over the moved quotient directly over the moved decimal point in the dividend.decimal point in the dividend.

4Martin-Gay, Prealgebra, 5ed

Divide 258.3 ÷ 2.8Divide 258.3 ÷ 2.8

Estimating When Dividing Estimating When Dividing DecimalsDecimals

ExactExact EstimateEstimate

28. 2583. - 252 63 - 56 70 - 56 140 -140 0

rounds to 3 300100

This is a reasonable answer.

92.25

Martin-Gay, Prealgebra, 5ed

There are patterns that occur when dividing by There are patterns that occur when dividing by powers of 10, such as 10, 100, 1000, and so on.powers of 10, such as 10, 100, 1000, and so on.

The decimal point moved The decimal point moved 1 place to the left.1 place to the left.

1 zero

3 zeros

The decimal point moved The decimal point moved 3 places to the left.3 places to the left.

The pattern suggests the following rule.The pattern suggests the following rule.

.45 6210

456.2

1 0000 4562

,.456.2

6Martin-Gay, Prealgebra, 5ed

Move the decimal point of the dividend to the leftleft the same number of places as there are zeroszeros in the power of 10.

Dividing Decimals by Powers of 10 Dividing Decimals by Powers of 10 such as 10, 100, or 1000, . . .such as 10, 100, or 1000, . . .

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 10 such as 100 is the same as multiplying by its reciprocal , or 0.01. 1

100463 7100

463 71

100463 7 0 01 4 637

.. . . .

To divide by a number is the same as multiplying by its reciprocal. 7