Why is 0.3 a rational number?

Answer 1

A rational number is one that can be represented as a fraction a/b.

0.3 = 3/10

ANY decimal that terminates is a rational number - just put all the digits after the decimal point over 1 followed by the same number of 0s as there are digits, eg 0.25 = 25/100 (two digits after decimal point, so two 0s after the 1, ie 100) and simplify: 25/100 = 1/4

Any decimal number that repeats one or more digits forever (eg 0.333... 0.181818..., 0.1666...) are also rational numbers as they can also be represented as a fraction (0.333... = 1/3; 0.181818... = 2/11; 0.1666... = 1/6)

If a decimal goes on forever but does not repeat any digits, then it cannot be represented as a fraction and is irrational, eg π = 3.1415926...

Answer 2

A "rational number" is any number that can be written as a fraction. This includes all whole numbers, numbers with a finite amount of decimals, and numbers with periodically repeating decimals.