What is a Rational Number?

A rational number is any number that can be expressed as a fraction where the numerator and the denominator are both integers and the denominator is not zero.

Fractions

Rational numbers can be written in the form a/b, where a and b are integers, and b is not equal to zero. For example, 3/4, -2/5, and 7/1 are all rational numbers.

Terminating and Repeating Decimals

Rational numbers can also be represented as decimal numbers. If the decimal form of a rational number ends, it is called a "terminating decimal." For example, 0.75 and 2.1 are rational numbers with terminating decimals. If the decimal form of a rational number repeats the same sequence of digits, it is called a "repeating decimal." For example, 0.333... (where the 3's repeat indefinitely) and 0.4545... are rational numbers with repeating decimals.

Relationship with Integers

All integers are rational numbers because they can be written as a fraction with a denominator of 1. For example, 5 can be written as 5/1, making it a rational number.

In conclusion, rational numbers are numbers that can be expressed as fractions or as terminating/repeating decimals, and they include all integers as well.