What is a rational number?
What is a rational number?
A rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p, and a non-zero denominator q. In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0.
Examples of rational numbers include:
- Fractions, such as 1/2, 2/3, and 3/4
- Integers, such as 1, 2, 3, and -4
- Decimals that terminate or repeat, such as 0.5, 0.3333..., and 1.23456789
Examples of numbers that are not rational include:
- Pi (π)
- The square root of 2 (√2)
- The golden ratio (φ)
Rational numbers are a subset of the real numbers. The real numbers are all of the numbers that can be represented on a number line. The rational numbers are the real numbers that can be expressed as fractions of two integers.
Rational numbers are important in mathematics and science. They are used in many different areas, including arithmetic, algebra, geometry, and calculus.
Here are some of the properties of rational numbers:
- The sum and difference of two rational numbers is always a rational number.
- The product of two rational numbers is always a rational number.
- The quotient of two rational numbers is always a rational number unless the denominator of the divisor is zero.
- Every rational number has a reciprocal, which is the number that, when multiplied by the original number, equals 1.
- Every rational number can be expressed as a decimal, but not every decimal is a rational number.
Rational numbers are very important in our everyday lives. We use them all the time to measure things, calculate prices, and make decisions.
