Section 1.1

Objectives

Copyright © 2013, 2009, and 2005, Pearson Education, Inc.

Introduction to Numbers, Notation, and Rounding

1. Name the digit in the specified space.2. Write whole numbers in standard and expanded form.3. Write the word name for a whole number.4. Graph a whole number on a number line.5. Use <, >, or = to write a true statement.6. Round numbers.7. Interpret bar graphs and line graphs.

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3Copyright © 2013, 2009, and 2005, Pearson Education, Inc.

Definition Sets: Numbers are classified into groups called sets.

Integers

Whole Numbers

Natural Numbers

…, –3, –2, –1, 0, 1, 2, 3, …

4Copyright © 2013, 2009, and 2005, Pearson Education, Inc.

Definition Subset: A set within a set.

Integers

Whole Numbers

Natural Numbers

…, –3, –2, –1, 0, 1, 2, 3, …


Definition Natural numbers: The natural numbers are 1, 2, 3,…

Integers

Whole Numbers

Natural Numbers

…, –3, –2, –1, 0, 1, 2, 3, …

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Objective 1 Name the digit in a specified place.

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Definition Periods: Place values are arranged in

groups of three called periods.

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Definition Standard Form: Numbers written using the place-value system are said to be in standard form.

When writing numbers in standard form, separate the periods with commas…like this

3,243,972

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Example 1 What digit is in the thousands place in 209,812?

Answer: 9

Explanation: The digit in the thousands place is the fourth digit from the right.

209,812

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Objective 2 Write whole numbers in standard and expanded form.

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Consider the meaning of each digit in 430…

4 x 100 +


Definition Expanded Form: Numbers written by multiplying each digit by its place value.

0 x 1 3 x 10 + or just 4 x 100 + 3 x 10

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Procedure

To write a number in expanded form, write each digit followed by its place-value name and a plus sign until you reach the last place, which is not followed by a plus sign.

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Example 2 Write the number in expanded form.

a. 57,483

Answer: 5 ten thousands + 7 thousands + 4 hundreds + 8 tens + 3 ones

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Example 2 Write the number in expanded form.

b. 4,705,208

Answer: 4 millions + 7 hundred thousands + 5 thousands + 2 hundreds + 8 ones

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Procedure

To convert from expanded form to standard form, write each digit in the place indicated by the corresponding place value. If the expanded form is missing a place value, write a 0 for that place value in the standard form.

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Example 3 Write the number in standard form.

a. 6 ten thousands + 9 thousands + 2 hundreds + 5 tens + 3 ones

Answer: 69,253

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Example 3 Write the number in standard form.

b. 9 millions + 2 ten thousands + 7 hundreds + 9 tens + 3 ones

Answer: 9,020,793 Explanation: Because hundred thousands and thousands were absent from the expanded form, we placed 0’s in the hundred thousands and thousands placed in the standard form.

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Objective 3 Write the word name for a whole number.

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To write the word name for a whole number, work from left to right through the periods.

Procedure

1. Write the word name of the number formed by the digits in the period.

2. Write the period name followed by a comma.

3. Repeat steps 1 and 2 for each period except the ones period. For the ones period, write only the word name formed by the digits. Do not follow the ones period with its name.

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Example 4 Earth is on average, 92,958,349 miles from the Sun. Write the word name for 92,958,349.

Answer: ninety-two million, nine hundred fifty-eight thousand, three hundred forty-nine.

Millions period Thousand period Ones period

9 2 9 5 8 3 4 9

ninety-two million nine hundred fifty-eight thousand

three hundred forty-nine

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Objective 4 Graph a whole number on a number line.

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To graph a whole number on a number line:

Procedure

Draw a dot on the mark for that number.

The arrow on the right indicates that the numbers increase indefinitely.

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Example 5 Graph 5 on a number line.

Solution: Draw a dot on the mark for 5.

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Objective 5 Use <, >, or = to write a true statement.

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12 = 12 is an equationThe equation is true.

But an equation can also be false.12 = 9 is an equation that is false.


Definition Equation: A mathematical relationship that contains an equal sign.

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Consider two inequality symbolsGreater than >Less than <


Definition Inequality: A mathematical relationship that contains an inequality symbol.

In comparing 12 and 9…

We can say: 12 is greater than 9 or 9 is less than 12

12 > 9 9 < 12

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a. 208 ? 205


Example 6 Use <, >, or = to write a true statement.

Answer: 208 > 205

Explanation: On a number line 208 is farther to the right than 205, so 208 is greater. We use the greater than symbol to open toward 208.

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Example 5 Use <, >, or = to write a true statement.

Answer: 48,995 < 49,000

Explanation: On a number line 49,000 is farther to the right than 48,995; so 49,000 is greater. We use the less than symbol toward 49,000.

b. 48,995 ? 49,000

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Objective 6 Round numbers.

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To round a number to a given place value…

Procedure

1. Identify the digit in the given place value.2. If the digit to the right of the given place

value is 5 or greater, round up by increasing the digit in the given place value by 1. If the digit to the right of the given place value is 4 or less, round down by keeping the digit in the given place value the same.

3. Change all of the digits to the right of the rounded place value to zeros.

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When we round a number, we must determine a place value to round to; often the place value will be specified. Let’s round 22,927,896 to the nearest million.

A number line can be helpful.

First we determine whether 22,927,896 is closer to the exact million greater than 22,927,896, which is 23,000,000

…or the exact million less than 22,927,896, which is 22,000,000

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Example 7 Round 43,572,991 to the specified place.

Solution: 43,572,991

a. hundred thousands

hundred thousands

Answer: 43,600,000

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Example 7


b. ten thousands

ten thousands

Answer: 43,570,000

Round 43,572,991 to the specified place.

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Example 7


c. millions

millions

Answer: 44,000,000


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Example 7


d. hundreds

hundreds

Answer: 43,573,000


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Example 8 Round each number so that there is only one nonzero digit.

Solution: 36,568

a. 36,568

farthest left

Answer: 40,000

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Solution: 621,905

b. 621,905

farthest left

Answer: 600,000

Example 8 Round each number so that there is only one nonzero digit.

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Objective 7 Interpret bar graphs and line graphs.

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Example 9 Use this graph, which shows the five states with the highest revenues for public education in 2006 - 2007.

Answer: $28,893,216a. What revenue did Florida generate?

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Answer: Californiab. Which state had the greatest revenue?

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Answer: $44,000,000c. Round Texas’ revenue to the nearest million.

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Example 10 Use the following graph, which shows average tuition and fees at two-year colleges.

Answer: $756

a. What were the average tuition and fees per semester in ‘89-’90?

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Answer: $400

b. Round the average tuition and fees per semester in ‘79-’80 to the nearest hundred.

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Answer: The cost of tuition has increased over the years (nearly doubling every decade.)

c. What general trend does the graph indicate?

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Section 1.1

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