CHAPTER

3Decimal Notation

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3.1 Decimal Notation, Order, and Rounding3.2 Addition and Subtraction3.3 Multiplication3.4 Division3.5 Converting from Fraction Notation to Decimal

Notation3.6 Estimating3.7 Applications and Problem Solving

OBJECTIVES

3.1 Decimal Notation, Order, and Rounding

dUse < or > for to write a true statement in a situation like 6 10.

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a Given decimal notation, write a word name.b Convert between decimal notation and fraction

notation.c Given a pair of numbers in decimal notation, tell

which is larger.d Round decimal notation to the nearest thousandth,

hundredth, tenth, one, ten, hundred, or thousand.

3.1 Decimal Notation, Order, and Rounding

a Given decimal notation, write a word name.

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3.1 Decimal Notation, Order, and Rounding

aGiven decimal notation,

write a word name.

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thousandths

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

a Given decimal notation, write a word name.

1

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a. Write a word name for 1788.045.Answer: One thousand, seven hundred eighty-eight and forty-five thousandths

b. The life expectancy at birth in the U.S. is projected to be 79.2 years in 2015. Write the word name for 79.2

Answer: Seventy-nine and two tenths

3.1 Decimal Notation, Order, and Rounding

bConvert between decimal notation and fraction notation.

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EXAMPLE

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

2

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a. Write fraction notation for 0.876. Do not simplify.

For a number like 0.876, we generally write a 0 before the decimal point to draw attention to the presence of the decimal point.

3.1 Decimal Notation, Order, and Rounding

Convert between decimal notation and fraction notation.

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b. Write fraction notation for 23.78. Do not simplify.

100

2378

c. Write fraction notation for 5.6789. Do not simplify.

000,10

789,56

3.1 Decimal Notation, Order, and Rounding

bConvert between decimal notation and fraction notation.

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To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000, and so on,

a) count the number of zeros, and

b) move the decimal point that number of places to the left. Leave off the denominator.

3.1 Decimal Notation, Order, and Rounding

bConvert between decimal notation and fraction notation.

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EXAMPLE

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

3

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3.1 Decimal Notation, Order, and Rounding

To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000, and so on,

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Write decimal notation

000,10

089,67

Answer: 7.43

a. 100

743 b.

Answer: 6.7089

c. 000,10

830

Answer: 0.0830

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

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If a mixed numeral has a fractional part with a denominator that is a power of ten, such as 10, 100, or 1000, and so on, we first write the mixed numeral as a sum of a whole number and a fraction. Then we convert to decimal notation.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

4

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3.1 Decimal Notation, Order, and Rounding

cGiven a pair of numbers in decimal notation, tell which is larger.

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To compare two numbers in decimal notation, start at the left and compare corresponding digits moving from left to right. If two digits differ, the number with the larger digit is the larger of the two numbers.

To ease the comparison, extra zeros can be written to the right of the last decimal place.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

c Given a pair of numbers in decimal notation, tell which is larger.

5

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EXAMPLE

3.1 Decimal Notation, Order, and Rounding

c Given a pair of numbers in decimal notation, tell which is larger.

6

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a. Which of 2.04 and 2.039 is larger?

Answer: 4>3, thus, 2.04 is larger than 2.039

b. Which of 21.006 and 21.05 is larger?

Answer: 5>0, thus, 21.05 is larger than 21.006

3.1 Decimal Notation, Order, and Rounding

dRound decimal notation

to the nearest thousandth,

hundredth, tenth, one, ten, hundred, or thousand.

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To round to a certain place:a) Locate the digit in that place.b) Consider the next digit to the right.c) If the digit to the right is 5 or higher, round up. If the digit to the right is 4 or lower, round down.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

d Round decimal notation to the nearest thousandth,hundredth, tenth, one, ten, hundred, or thousand.

7

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Round 3872.2459 to the nearest thousandth, hundredth,tenth, one, ten, hundred, and thousand.