Download Prealgebra & Introductory Algebra

1.2
Place Value, Names
for Numbers, and
Reading Tables
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Place Value
Ten-millions
Millions
Hundred-thousands
Ten-thousands
Thousands
Hundreds
Tens
Ones
Hundred-millions
Billions
Ten-billions
Hundred-billions
The position of each digit in a number determines its place value.
3
5
6
8
9
4
0
2
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
2
Writing a Number in Words
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.
Hundred-thousands
Ten-thousands
Thousands
Hundreds
Tens
Ones
Ones
Millions
Thousands
Ten-millions
Hundred-millions
Millions
Billions
Ten-billions
Hundred-billions
Billions
3
5
6
8
9
4
0
2
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
3
Writing a Number in Words
Ten-thousands
Thousands
Hundreds
Tens
Ones
3 5
Hundred-thousands
Millions
Ten-millions
Hundred-millions
Billions
Ten-billions
Hundred-billions
To write a whole number in words, write the number in each period
followed by the name of the period.
6
8
9
4
0
2
thirty-five million, six hundred eighty-nine thousand, four hundred two
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
4
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
5
Expanded Form
Standard Form
4,786
Expanded Form
=
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
6
Comparing Whole Numbers
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
7
Comparing Numbers
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.
0
1
2
3
4
5
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
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
8
Comparing Numbers . . .
2 is less than 5
can be written in symbols as
2<5
5 is greater than 2
is written as
5>2
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
9
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
10
Reading Tables
Most Medals Olympic Winter (1924 – 2002) Games
Gold
Silver
Bronze
Total
Germany
107
104
86
297
Russia
113
83
78
274
Norway
94
92
74
260
USA
69
71
51
191
Austria
41
57
64
162
Source: The Sydney Morning Herald, Flags courtesy of www.theodora.com/flags used with permission
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
11