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Place Value and Names for Numbers

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Section 1.2

Place Value and Names for Numbers

Hundred-billions

Ten-billions

Billions

Hundred-millions

Ten-millions

Millions

Hundred-thousands

Ten-thousands

Thousands

Hundreds

Tens

Ones

3 5 6 8 9 4 0 2

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

Martin-Gay, Prealgebra, 5ed

Billions

Millions

Thousands

Ones

Hundred-billions

Ten-billions

Billions

Hundred-millions

Ten-millions

Millions

Hundred-thousands

Ten-thousands

Thousands

Hundreds

Tens

Ones

3 5 6 8 9 4 0 2

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

Martin-Gay, Prealgebra, 5ed

Hundred-billions

Ten-billions

Billions

Hundred-millions

Ten-millions

Millions

Hundred-thousands

Ten-thousands

Thousands

Hundreds

Tens

Ones

3 5 6 8 9 4 0 2

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

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

Helpful Hint

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

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

Martin-Gay, Prealgebra, 5ed

Standard Form

Expanded Form

4,786 = 4000 + 700 + 80 + 6

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

Martin-Gay, Prealgebra, 5ed

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

0

1

2

3

4

5

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

Martin-Gay, Prealgebra, 5ed

0

1

2

3

4

5

For any two numbers graphed on a number line, the number to the right is the greater number, and the number to the left is the smaller number.

2 is to the left of 5, so 2 is less than 5

5 is to the right of 2, so 5 is greater than 2

Martin-Gay, Prealgebra, 5ed

2 is less than 5

can be written in symbols as

2 < 5

5 is greater than 2

is written as

5 > 2

Martin-Gay, Prealgebra, 5ed

Helpful Hint

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

2 < 5 and 5 > 2

are both true statements.

Martin-Gay, Prealgebra, 5ed

Germany

Russia

Norway

USA

Austria

Most Medals Olympic Winter (1924 – 2002) Games

Source: The Sydney Morning Herald

Flags courtesy of www.theodora.com/flags used with permission