CHAPTER OUTLINE

3Decimals

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3.1 Decimal Notation and Rounding3.2 Addition and Subtraction of Decimals3.3 Multiplication of Decimals and Applications with

Circles3.4 Division of Decimals3.5 Fractions, Decimals, and the Order of Operations

Section 3.4 Homework questions?

Section

Objectives

3.4 Division of Decimals

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1. Division of Decimals2. Rounding a Quotient3. Applications of Decimal Division

PROCEDURE Dividing a Decimal by a Whole Number

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To divide by a whole number:Step 1 Place the decimal point in the quotient directly above the decimal point in the dividend.Step 2 Divide as you would whole numbers.

Example 1 Dividing by a Whole Number

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Divide and check the answer by multiplying.

Section 3.4 Division of Decimals

1. Division of Decimals

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When dividing decimals, we do not use a remainder. Instead we insert zeros to the right of the dividend and continue dividing.

Example 2 Dividing by an Integer

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Divide and check the answer by multiplying.

Example 3 Dividing by an Integer

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Divide and check the answer by multiplying.

Section 3.4 Division of Decimals

1. Division of Decimals

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Sometimes when dividing decimals, the quotient follows a repeated pattern. The result is called a repeating decimal.

Example 4 Dividing Where the Quotient Is a Repeating Decimal

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ExampleSolution:

4 Dividing Where the Quotient Is a Repeating Decimal

(continued)

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The quotient is 0.05666 . . . .To denote the repeated pattern, we often use a bar over the first occurrence of the repeat cycle to the right of the decimal point.That is,

Avoiding Mistakes

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In Example 4, notice that the repeat bar goes over only the 6. The 5 is not being repeated.

Section 3.4 Division of Decimals

1. Division of Decimals

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The numbers and are examples of repeating decimals. A decimal that “stops” is called a terminating decimal.

Example 6 Dividing Decimals

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PROCEDURE Dividing by a Power of 10

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To divide a number by a power of 10, move the decimal point to the left the same number of places as there are zeros in the power of 10.

Example 8 Dividing by a Power of 10

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Section

1. Divide: 502.96 ÷ 8.

2. Divide: 3 ÷ 20

3. Divide: 0.64 ÷ (- 0.4)

4. Divide: -70 ÷ (- 0.6)

5. Divide: 0.0039 ÷ 10

3.4 Try these on your own:

Example 9 Rounding a Repeating Decimal

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Section 3.4 Division of Decimals

2. Rounding a Quotient

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Sometimes we may want to round a quotient to a given place value. To do so, divide until you get a digit in the quotient one place value to the right of the roundingplace. At this point, you can stop dividing and round the quotient.

Example 10 Rounding a Quotient

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Round the quotient to the tenths place.

Example 12 Using Division to Find a Rate of Speed

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In a recent year, the world-record time in the men’s 400-m run was 43.2 sec. What is the speed in meters per second? Round to one decimal place. (Source: International Association of Athletics Federations)

Section

1. Round the quotient to the indicated place value: 42.68 ÷ 5.1; hundredths.

2. A 46.5 – ft. cable is to be cut into 6 pieces of equal length. How long is each piece?

3.4 Try these on your own: