Place Value and Names Place Value and Names for Numbersfor Numbers

Section 1.2

The position of each digit in a number The position of each digit in a number determines its place value.determines its place value.

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A whole number such as 35,689,402 is written in A whole number such as 35,689,402 is written in standard standard formform. The columns separate the digits into groups of threes. . The columns separate the digits into groups of threes. Each group of three digits is a Each group of three digits is a periodperiod..

MillionsMillions ThousandsThousandsBillionsBillions OnesOnes

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To write a whole number in words, write the To write a whole number in words, write the number in each period followed by the name of number in each period followed by the name of the period.the period.

thirty-five million, six hundred eighty-nine thirty-five million, six hundred eighty-nine thousand, four hundred twothousand, four hundred two

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The name of the ones period is not used The name of the ones period is not used when reading and writing whole when reading and writing whole numbers. numbers.

Also, the word Also, the word “and”“and” is not used when is not used when reading and writing whole numbers. It is reading and writing whole numbers. It is used when reading and writing mixed used when reading and writing mixed numbers and some decimal values as numbers and some decimal values as shown later.shown later.

Helpful HintHelpful Hint

5Martin-Gay, Prealgebra, 5ed

The place value of a digit can be used to The place value of a digit can be used to write a number in write a number in expanded form. expanded form. The The expanded form of a number shows each expanded form of a number shows each digit of the number with its place value.digit of the number with its place value.

4,786 = 4000 + 700 + 80 + 6

Standard FormStandard Form Expanded FormExpanded Form

6Martin-Gay, Prealgebra, 5ed

Comparing Whole NumbersComparing Whole Numbers

We can picture whole numbers as We can picture whole numbers as equally spaced points on a line called equally spaced points on a line called the number line.the number line.

A whole number is graphed by placing A whole number is graphed by placing a dot on the number line. The graph of a dot on the number line. The graph of 4 is shown.4 is shown.

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7Martin-Gay, Prealgebra, 5ed

Comparing Numbers . . .Comparing Numbers . . .

For any two numbers graphed on a For any two numbers graphed on a number line, the number to the number line, the number to the rightright is is the the greater numbergreater number, and the number to , and the number to the the leftleft is the is the smaller numbersmaller number..

2 is to the 2 is to the leftleft of 5, so 2 of 5, so 2 is less thanis less than 5 5

5 is to the 5 is to the rightright of 2, so 5 of 2, so 5 is greater thanis greater than 2 2

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8Martin-Gay, Prealgebra, 5ed

Comparing Numbers . . .Comparing Numbers . . .

2 is less than 52 is less than 5

can be written in symbols ascan be written in symbols as

2 < 52 < 5

5 is greater than 25 is greater than 2

is written asis written as

5 > 25 > 2

9Martin-Gay, Prealgebra, 5ed

One way to remember the meaning of One way to remember the meaning of the inequality symbols the inequality symbols << and and >> is to is to think of them as arrowheads think of them as arrowheads ““pointing” pointing” toward the smaller number. For toward the smaller number. For example, example,

2 < 52 < 5 and and 5 > 25 > 2

are both true statements.are both true statements.

Helpful HintHelpful Hint

10Martin-Gay, Prealgebra, 5ed

11

Reading TablesReading Tables

GoldGold SilverSilver BronzeBronze TotalTotal

107107 104104 8686 297297

113113 8383 7878 274274

9494 9292 7474 260260

6969 7171 5151 191191

4141 5757 6464 162162

Source: The Sydney Morning HeraldFlags courtesy of www.theodora.com/flags used with permission

GermanyGermany

RussiaRussia

NorwayNorway

USAUSA

AustriaAustria

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