Page 119 - ArithBook5thEd ~ BCC

Chapter 4

Decimals and Percents

Decimals are mixed numbers in which the proper fractional part has adenominator which is 10, or 100,
or 1000, or, more generally, a power of 10. Here are some powers of 10:

0
10 =1
1
10 =10
2
10 =100
3
10 =1000
4
10 =10000
n
10 =1 followed by n 0’s.

The number above and to the right of 10 is the exponent,or power,and indicates the number of times
that 10 appears as a factor. Thus

3
10 =10 × 10 × 10 = 1000,

and so forth.
Here are some examples of mixed numbers in which the denominator of the fractional part is a power
of ten, together with their representations as decimals:

3
1 = 1.3
10
37
21 = 21.37
100
21
13 = 13.021
1000
The decimal point (which looks like the period at the end of a sentence) separates the whole number
part from the proper fractional part. The digits to the right of the decimal point represent the fractional
part according to the following rule:
• the digits to the right of the decimal point constitute the numerator;

• the number of digits to the right of the decimal point is the power of 10 which constitutes the
denominator.

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