Basic Mathematics for College Students

4.1 An Introduction to Decimals 321

4 Compare decimals using inequality symbols.

To develop a way to compare decimals, let’s consider 0.3 and 0.271. Since 0.271
contains more digits, it may appear that 0.271 is greater than 0.3. However, the
opposite is true. To show this, we write 0.3 and 0.271 in fraction form:

Now we build 103 into an equivalent fraction so that it has a denominator of 1,000, like

0.271

271

1,000

0.3

3

10

that of

Since it follows that This observation suggests a quicker
method for comparing decimals.

1,000^300 1,000^271 , 0.30.271.

0.3

3

10



100

100



300

1,000

271

1,000^.

Comparing Decimals

To compare two decimals:

1. Make sure both numbers have the same number of decimal places to the right
   of the decimal point. Write any additional zeros necessary to achieve this.


2. Compare the digits of each decimal, column by column, working from left
   to right.


3. If the decimals are positive:When two digits differ, the decimal with the
   greater digit is the greater number.If the decimals are negative:When two
   digits differ, the decimal with the smaller digit is the greater number.

EXAMPLE (^5) Place an or symbol in the box to make a true statement:
a.1.2679 1.2658 b.54.9 54.929 c.
StrategyWe will stack the decimals and then, working from left to right, we will
scan their place-value columns looking for a difference in their digits.
WHYWe need only look in that column to determine which digit is the greater.
Solution
a.Since both decimals have the same number of places to the right of the
decimal point, we can immediately compare the digits, column by column.
1.26 9
1.26 8
Same digit
Same digit
Same digit These digits are different: Since 7 is greater than 5, it
follows that the first decimal is greater than the second.
Thus, 1.2679 is greater than 1.2658 and we can write
b.We can write two zeros after the 9 in 54.9 so that the decimals have the same
number of digits to the right of the decimal point. This makes the comparison
easier.
54.9 0
54.9 9
As we work from left to right, this is the first column in which the digits differ.
Since it follows that 54.929 is greater than 54.9 (or 54.9 is less than
54.929) and we can write 54.954.929.

2 0,

2

0

1.26791.2658.

5

7

10.419 10.45

 

Self Check 5

Place an or symbol in the

box to make a true statement:

a.3.4308 3.4312

b.678.3409 678.34

c.

Now TryProblems 49, 55, and 59

703.8 703.78