Basic Mathematics for College Students

404 Chapter 4 Decimals

86. TELESCOPES To change the position of a
    focusing mirror on a telescope, an adjustment knob
    is used. The mirror moves 0.025 inch with each
    revolution of the knob. The mirror needs to be

moved 0.2375 inch to improve the sharpness of the

image. How many revolutions of the adjustment

knob does this require?

SECTION 4.5 Fractions and Decimals

A fraction and a decimal are said to be equivalent

if they name the same number.

To write a fraction as a decimal, divide the

numerator of the fraction by its denominator.

Sometimes, when finding the decimal equivalent

of a fraction, the division process ends because a

remainder of 0 is obtained. We call the resulting

decimal a terminating decimal.

DEFINITIONS AND CONCEPTS EXAMPLES

Write as a decimal.

We divide the numerator by the denominator because a fraction bar

indicates division: means.

Thus,^35 0.6. We say that 0.6 is the decimal equivalentof.^35

Write a decimal point and one additional

zero to the right of 3.

Since a zero remainder is obtained, the

result is a terminating decimal.



0.6

5  3 .0

 30

0

(^353)  5
3
5
If the denominator of a fraction in simplified form
has factors of only 2’s or 5’s, or a combination of
both, it can be written as a decimal by multiplying
it by a form of 1.The objective is to write the
fraction in an equivalent form with a denominator
that is a power of 10, such as 10, 100, 1,000, and so
on.
Write as a decimal.
Since we need to multiply the denominator of by 4 to obtain a
denominator of 100, it follows that should be
the form of 1 that is used to build.
Multiply by 1 in the form of.
Multiply the numerators.
Multiply the denominators.
0.12 Write the fraction as a decimal.



12

100

4

4

3

(^25)

3

25



3

25



4

4

3

25

4

4

3

25

3

25

Sometimes, when we are finding the decimal

equivalent of a fraction, the division process never

gives a remainder of 0. We call the resulting

decimal a repeating decimal.

An overbarcan be used instead of the three dots

... to represent the repeating pattern in a
repeating decimal.

Write as a decimal.

Thus,^56 0.8333... , or, using an overbar, we have 65 0.83.

Write a decimal point and three

additional zeros to the right of 5.

It is apparent that 2 will continue to reappear as the

remainder. Therefore, 3 will continue to reappear in the

quotient. Since the repeating pattern is now clear, we can

 stop the division.

0.833

6  5 .000

 48

20

 18

20

 18

2

5

6

When a fraction is written in decimal form, the

result is either a terminating or repeating decimal.

Repeating decimals are often rounded to a

specified place value.

The decimal equivalent for is 0.454545 ....Round it to the

nearest hundredth.

Rounding digit: hundredths column.

Test digit: Since 4 is less than 5, round down.

Thus, 115 0.45.

5

11

0.454545...

5

11