Sunday, 20 July 2008

Numbers | Rational or Irrational

Numbers can be like humans, having rational and irrational nature.
How is it so...

First, we need to know what is the difference between rational and irrational number?

Rational number is any number that can be represented as a ratio of two integers (exception is when the denominator equals zero).

Example of rational number is 1 / 3. Although 1 / 3 gives 0.333333........ , with the decimal number 3 going endlessly, it is still a rational number.

Irrational number is a number that can never be expressed as a ratio of integers.

Example of irrational number is "pi" which has the decimal numbers going endlessly, and is only approximated by the fraction 22/7.

Another irrational number is the famous exponential number (Euler's number) e.

Application of the "pi" includes the calculation of the area of a circle and the perimeter of a circle.

For the irrational number e, it is used to model the electrical characteristics of a diode or any semiconductor device or electronic component.

Having known the nature of numbers being rational and irrational, we are now in a better position to appreciate maths. When to use decimal presentation or fractional presentation of numbers comes with this understanding of rational and irrational concept.

Therefore treat maths (and numbers) with respect as they can behave similar to human being.

1 comment:

Ordinate said...

I ma here to discuss about irrational number as a real number that cannot be expressed as a rational number, ie. a number that cannot be written as a simple fraction - the decimal goes on forever without repeating.
Example: Pi is an irrational number