Difference Between Rational and Irrational Numbers

What is the difference Between Rational and Irrational Numbers?

Rational Numbers: – Every integer and fractions are rational numbers. It can always be denoted as p/q, where p and q are integers and q is not equal to 0.

Thus for example the rationals include {0, 5/2, -18, -4/3, 27/5}. We unually write rational numbers in their lowest terms, for example 8/10 is usually written 4/5. We commonly write rationals in decimal form, so that 1/4 is the same as 0.25, 13/8 = 1.625 and 4/5 = 0.8. Some rationals, however, when written in decimal form don’t stop a few places after the decimal. For example 1/3 = 0.333…, 10/11 = 0.909090… and 3/13 = 0.230769230769… When you write a rational number in decimal form you obtain either a decimal that stops after a finite number of terms, or a pattern that repeats as in the latter three examples.

Irrational Numbers: - Infinite non-recurring decimal number can be expressed as an irrational number.

If you construct a decimal that does not terminate and does not repeat it is not a rational number. For example 0.102003000400005… Numbers that are not rational are called irrational. The most famous of these is the ratio of the circumference of a circle to its diameter, called . is approximately 3.14159265358979323846; no matter how far we take the decimal expansion, it never repeats. Another irrational number is  which is approximately 1.4142135623731.

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