Basic Mathematics for College Students

378 Chapter 4 Decimals

Using Your CALCULATOR The Fixed-Point Key

After performing a calculation, a scientific calculator can round the result to a

given decimal place. This is done using the fixed-point key.As we did in

Example 7, let’s find the decimal equivalent of and round to the nearest

thousandth. This time, we will use a calculator.

First, we set the calculator to round to the third decimal place (thousandths)

by pressing 3. Then we press 2 7

Thus,. To round to the nearest tenth, we would fix 1; to round to the

nearest hundredth, we would fix 2; and so on. After using the FIX feature,

don’t forget to remove it and return the calculator to the normal mode.

Graphing calculators can also round to a given decimal place. See the owner’s

manual for the required keystrokes.

2

7 0.286

2nd FIX   0.286

2

7

4 Graph fractions and decimals on a number line.

A number line can be used to show the relationship between fractions and their

decimal equivalents. On the number line below, sixteen equally spaced marks are used

to scale from 0 to 1. Some commonly used fractions that have terminating decimal

equivalents are shown. For example, we see that^18 0.125and 1613 0.8125.

(^0) –– 1
16
(^1) –
8
––^3
16
(^1) –
4
––^5
16
(^3) –
8
––^7
16
(^1) –
2
––^9
16
(^5) –
8
(^11) ––
16
(^13) ––
16
(^15) –– 1
16
(^3) –
4
(^7) –
8
0.06250.1250.18750.250.31250.3750.43750.5 0.56250.6250.68750.750.81250.8750.9375
On the next number line, six equally spaced marks are used to scale from 0 to 1.
Some commonly used fractions and their repeating decimal equivalents are shown.
(^1) –
2
(^01) –
6
(^5) –
6
(^1) –
3
(^2) –
3
1
0.16 0.3 0.6 0.83
5 Compare fractions and decimals.
To compare the size of a fraction and a decimal, it is helpful to write the fraction in its
equivalent decimal form.
EXAMPLE (^8) Place an , , or an symbol in the box to make a true
statement: a. 0.91 b. c. 2.25
StrategyIn each case, we will write the given fraction as a decimal.
WHYThen we can use the procedure for comparing two decimals to determine
which number is the larger and which is the smaller.
Solution
a.To write as a decimal, we divide 4 by 5.
Write a decimal point and one additional zero to the right of 4.
Thus,^45 0.8.

0.8

(^5) 4.0
 40
0
4
5

9

4

1

3

0.35

4

5

 

Self Check 8

Place an , , or an symbol in

the box to make a true

statement:

a. 0.305

b.

c. 2.75

Now TryProblems 67, 69, and 71

11

4

7

9

0.76

3

8