Q:
# What are rational and irrational numbers?

**Rational numbers are numbers that can be expressed as the ratio of two integers, whereas irrational numbers cannot be expressed as a ratio of integers.** Irrational numbers expressed as decimals generate an unending series of numbers after the decimal point that never falls into a repeating pattern.

Because a ratio can written as a fraction, any rational number can be expressed as a fraction. For example, the number 7 can be written as 7/1. The number 1.25 can be written as 5/4. The repeating decimal .333... can be written as 1/3. These are all rational numbers. Complex fractions, such as 97/98, often result in a long series of numbers after the decimal point, but the series must ultimately terminate or fall into a repeating pattern. The fact that the number can be expressed as the ratio of two whole numbers means it is, by definition, rational.

Irrational numbers, such a pi, cannot be written as the ratio of two whole numbers. While the fraction 7/22 is often used as a substitute for pi, it is only an approximation. Pi is the ratio of the circumference of any circle to its diameter. Though it has been calculated out to billions of decimal places, no consistently repeating pattern has ever been found. Though irrational numbers may seem like rarities, there are an infinite number of them. Taking the square root of any number that is not a perfect square always yields an irrational number.

Learn more about Numbers-
Q:
## What does "rational number" mean?

A: A rational number is a real number that can be expressed as a fraction or ratio of two integers where the denominator is not zero. Whole numbers, finite de... Full Answer >Filed Under: -
Q:
## What is the difference between odd and even numbers?

A: Even numbers are integers that when divided by two produce another integer. Odd numbers are integers that are not divisible by two; in other words, when di... Full Answer >Filed Under: -
Q:
## How do you place rational numbers in order from least to greatest on a number line?

A: Rational numbers are any numbers that can be expressed by a fraction with integers in both the numerator and the denominator. The amount of time and paper ... Full Answer >Filed Under: -
Q:
## Are all integers rational numbers?

A: All integers are rational numbers. A rational number is in the form a/b, where "a" and "b" are integers, and "b" is not equal to zero. Integers are a subse... Full Answer >Filed Under: