Basic Mathematics for College Students

Using a process known as graphing,we can represent a single number or a set of
numbers on a number line.The graph of a numberis the point on the number line that
corresponds to that number.To graph a numbermeans to locate its position on the
number line and highlight it with a heavy dot. The graphs of 5 and 8 are shown on the
number line below.

1.1 An Introduction to the Whole Numbers 5

EXAMPLE (^4) Write each number in expanded form:
a.85,427 b.1,251,609
Strategy Working from left to right, we will give the place value of each digit and
combine them with symbols.
WHY The term expanded form means to write the number as an addition of the
place values of each of its digits.
Solution
a.The expanded form of 85,427 is:
8 ten thousands 5 thousands 4 hundreds 2 tens 7 ones
which can be written as:
8 0,000  5 ,000  400  20  7
b.The expanded form of 1,251,609 is:
Since 0 tens is zero, the expanded form can also be written as:
which can be written as:
1 ,000,000  2 00,000  5 0,000  1 ,000  600  9

9

ones

6

hundreds

1

thousand

5 ten

thousands

2 hundred

thousands

1

million

9

ones

0

tens

6

hundreds

1

thousand

5 ten

thousands

2 hundred

thousands

1

million

Self Check 4

Write 708,413 in expanded form.

Now TryProblems 49, 53, and 57

4 Compare whole numbers using inequality symbols.

Whole numbers can be shown by drawing points on a number line.Like a ruler, a
number line is straight and has uniform markings. To construct a number line, we begin
on the left with a point on the line representing the number 0. This point is called the
origin.We then move to the right, drawing equally spaced marks and labeling them
with whole numbers that increase in value. The arrowhead at the right indicates that
the number line continues forever.

0 1

Origin

2 3 45 Arrowhead

A number line

6789

0 1 2 3 45 6789

As we move to the right on the number line, the numbers increase in value.
Because 8 lies to the right of 5, we say that 8 is greater than 5. The inequality symbol
(“is greater than”) can be used to write this fact:

Read as “8 is greater than 5.”

Since 85, it is also true that 58. We read this as “5 is less than 8.”

8  5