The string of numerals to the right of the point represents the sum
SB= (b 1 × 10 −^1 )+ (b 2 × 10 −^2 )+ (b 3 × 10 −^3 )+ ··· + (bn × 10 −n)
The entire number is represented by the sum S=SA+SB. Mathematicians like to use the nonitalic, upper-
case Greek letter sigma (Σ) to represent sums of many numbers. We can get fancy and write the above
expressions like this:
ΣA= (am × 10 m−^1 )+ ··· + (a 3 × 102 )+ (a 2 × 101 )+ (a 1 × 100 )
and
ΣB= (b 1 × 10 −^1 )+ (b 2 × 10 −^2 )+ (b 3 × 10 −^3 )+ ··· + (bn × 10 −n)
The entire number is therefore the sum Σ=ΣA+ΣB. It’s a good idea to remember this summation symbol.
You’ll come across it when you study higher algebra, precalculus, and calculus.
Terminating Decimals
All of the decimal expressions you’ll see in everyday situations have a finite number of digits
to the right of the decimal point. The most common example is the notation for dollars and
cents, where there are always two digits to the right of the decimal point. Any further dig-
its, if you want to write them, are all ciphers. A numeral of this sort is called a terminating
decimal.
Tenths, hundredths, or whatever
In a terminating decimal, the digits to the right of the decimal point always represent a frac-
tion having a denominator that is some power of 10. If there’s one digit, it represents 10ths;
if there are two digits, they represent 100ths; if there are three digits, they represent 1,000ths;
and so on, as far as you want to go. For example,
- 0.7 represents 7/10
- 0.72 represents 72/100
- 0.729 represents 729/1,000
- 0.7294 represents 7,294/10,000
- 0.72941 represents 72,941/100,000
When you have a denominator of 10n, where n is a positive integer, it is the equivalent of
multiplying by 10−n. You can also write the above examples as
- 0.7 represents 7 × 10 −^1
- 0.72 represents 72 × 10 −^2
- 0.729 represents 729 × 10 −^3
- 0.7294 represents 7,294 × 10 −^4
- 0.72941 represents 72,941 × 10 −^5
Terminating Decimals 99
