Algebra Demystified 2nd Ed

66 algebra De mystif ieD

A decimal number is convenient notation for the sum of fractions. For example

the decimal number 0.183 is the sum of three fractions.

1

10

8

100

3

1000

1

10

100

100

8

100

10

10

3

1000

++ =⋅+⋅+=^100 +^8003

1000

183

1000

+ =

As you can see, the denominators of these fractions are powers of 10. Here

are the powers of 10 that we will use most in this chapter.

10 10

10 100

10 1000

1

2

3

=

=

=

104 =10 000,

For now, we will learn how to convert a decimal number to its fraction form.

Later, we will learn rules for adding, subtracting, multiplying, and dividing with

decimal numbers.

The number in front of the decimal point is the whole number, and the

number behind the decimal point is the numerator of a fraction whose denomi-

nator is a power of 10. The denominator consists of 1 followed by one or more

zeros. The number of zeros is the same as the number of digits behind the deci-

mal point.

EXAMPLES

Rewrite the decimal number as a fraction.

2.8 = 2108 (one decimal place—one zero)

0.7695 = 7695

10 000,

(four decimal places—four zeros)

PRACTICE

Rewrite the decimal number as a fraction. If the decimal number is more

than 1, rewrite the number both as a mixed number and an improper frac-

tion. You do not need to simplify the answer.

1. 1.71 =


2. 34.598 =


3. 0.6 =


4. 0.289421 =

EXAMPLES

Rewrite the decimal number as a fraction.

PRACTICE

Rewrite the decimal number as a fraction. If the decimal number is more