Arithmetic
3 kinds of decimals
(1)
terminating decimals
(2)
repeating decimals
(3)
non-repeating decimals
Thm: terminating decimals and repeating decimals are fractions of integers. (quotient of integers)
Procedure:
Given a fraction, to find what kind of decimal it is, without dividing the decimal,
First, completely reduce the fraction to lowest terms, then find prime factorization of the denominator.
(1) If the prime factorization of the denominator has only 2's and/or 5's, then it is a terminating decimal.
In this case, the higher exponent of either 2 or 5 represents the exact number of decimal places.
(2) If the prime factorization of the denominator has any prime factor 3, 7, 11, 13, 17, 19 or greater,
then it is a repeating decimal.
For each of the fractions, without dividing, find the kind of decimal and if terminating, find the exact number of
decimal places. Then convert each fraction into a decimal and confirm the number of decimal places.
Ex1, 12
Ex2,
6
40
Ex3,
23
14
Ex4,
39
96
Ex5,
4
9
Ex6,
23
800
Ex7.
35
250
Ex8,
6
75
Ex9,
4
7