terminating decimals repeating decimals
Pi, the square root of 7, e, 1/3, and ______ irrational numbers, square roots, repeating decimals
Their denominators have prime factors of 2 or 5.
The only prime factors are 2 and 5.
In their simplest form the denominators have no prime factor other than 2 or 5.
terminating decimals repeating decimals
Pi, the square root of 7, e, 1/3, and ______ irrational numbers, square roots, repeating decimals
sqrt(2), sqrt(3), sqrt(5), 2+sqrt(3) pi, e
Their denominators have prime factors of 2 or 5.
The only prime factors are 2 and 5.
In their simplest form the denominators have no prime factor other than 2 or 5.
If the denominator of the fraction has any prime factor other than 2 or 5, then it has a decimal representation with a repeating sequence of digits. If the denominator is a product of any number of 2s or 5s then it can be represented as a terminating decimal.
There is at least one example: 4/5 = 0.8 5/4 = 1.25
All rational fractions - one integer divided by a non-zero integer - give rise to repeating or terminating decimals. If, for the fraction in its simplest form, the denominator can be expressed as a product of powers of only 2 and 5 then the decimal will terminate. If the denominator has any prime factor other than 2 or 5 the decimal will be recurring. All non-rational fractions will have infinite, non-recurring decimal representations.
If a fraction, in its simplest form has a denominator whose only prime factors are 2 or 5, then the fraction is terminating. If the denominator has any other prime factor then the decimal is repeating.
To sum this answer up you half to turn the fraction into a decimal and if it ends that is terminating but if it keeps going it is called a repeating decimal EXAMPLES Terminating- 5/10=.5 Repeating- 1/3=.3333 (bar notation over the 3)
Rational numbers will become either a terminating decimal (if the denominator has prime factors of 2 and/or 5 only) or a decimal that recurs one or more digits (possibly after one or more digits that do not recur). Examples: 1/2 = 0.5 (terminates) 1/3 = 0.333.... (3 recurs) 1/6 = 0.1666.... (6 recurs after the initial non-recurring 1) 1/7 = 0.142857142857142857.... (142857 recurs)