Periodic fraction

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of repeating terms is called the period of the continued fraction. All nontrivial periodic continued fractions represent irrational numbers.

1. How do you know if a fraction is periodic?
2. What is an example of a repeating fraction?
3. What is periodic decimals in math?

How do you know if a fraction is periodic?

To find out whether a fraction will have a terminating or recurring decimal, look at the prime factors of the denominator when the fraction is in its most simple form. If they are made up of 2s and/or 5s, the decimal will terminate.

What is an example of a repeating fraction?

Cyclic Numbers. Most of you are already familiar with the repeating decimal digits of fractions like one third (1/3) or two thirds (2/3) which have these never ending strings of threes and sixes: 1 / 3 = 0.3333333333... and 2 / 3 = 0.6666666666...

What is periodic decimals in math?

A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely).