Fundamentals of Mathematics, 2008a

341
The value of the third position to the right of the units digit is 1
10 of 1
100 , or
1
10 · 1
100 = 1
10
= 1
3 1000
This pattern continues.
We can now see that if we were to write digits in positions to the right of the units positions, those positions
have values that are fractions. Not only do the positions have fractional values, but the fractional values are
all powers of 10 ( 10, 10 2 , 10 3 , . . . ) .
6.2.3 Decimal Fractions
Decimal Point, Decimal
If we are to write numbers with digits appearing to the right of the units digit, we must have a way of denoting
where the whole number part ends and the fractional part begins. Mathematicians denote the separation
point of the units digit and the tenths digit by writing a decimal point. The word decimal comes from
the Latin prex "deci" which means ten, and we use it because we use a base ten number system. Numbers
written in this form are called decimal fractions, or more simply, decimals.
Notice that decimal numbers have the sux "th."
Decimal Fraction
A decimal fraction is a fraction in which the denominator is a power of 10.
The following numbers are examples of decimals.
1. 42.6
The 6 is in the tenths position.
42.6 = 42 6
10
2. 9.8014
The 8 is in the tenths position.
The 0 is in the hundredths position.
The 1 is in the thousandths position.
The 4 is in the ten thousandths position.
9.8014 = 9 8014
10,000
3. 0.93
The 9 is in the tenths position.
The 3 is in the hundredths position.
0.93 = 93
100
note: Quite often a zero is inserted in front of a decimal point (in the units position) of a
decimal fraction that has a value less than one. This zero helps keep us from overlooking the
decimal point.
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