# Rational And irrational numbers?

Hey Yahoo i have recently begun learning about rational and irrational numbers in math and i can easily detect wether or not a number is rational however the definition confuses me.

A rational numer is said to be a number which can be expressed as a ratio of two integers in the form a/b where b is not equal to 0 and a and b have no common factors.

The first part makes sense in that a rational number is a ratio in which the answer is not infinite however the number 6/3 is a rational number as it is 0.5 which is a non integer however it terminates. But according to the definition it would not be rational as 6 and 3 share the common factor of 3. Am i misreading something or do i have something wrong. Please explain what the no common factor part means if i am wrong.

Relevance

The number 8 is a rational number because it can be written as the fraction 8/1.

Likewise, 3/4 is a rational number because it can be written as a fraction.

Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.

An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:

π = 3.141592…

square root of 2 = 1.414213…

• 355/113 will recur with a era of length decrease than 113. The definition wins the following and says that 355/113 is rational. the priority is in assuming that 355/113, which superficially imitates pi partly of its decimal representation, would not terminate. yet another challenge is in the actual undeniable actuality that the rationals and irrationals are disjoint instruments via their definitions. i'm curious as to why you idea that 355/113 does no longer recur?