Math K-Plus

Definition Of Rational Number

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What Is A Rational Number?

In mathematics, a Rational Number is any number that can be expressed as a Fraction p/q (integer number p divided by integer number q); the denominator q can not equal zero. Another important fact of arithmetic, q may be equal to 1, which means every integer is a rational number. Simple example: 10/1 = 10 and an earlier lesson showed us that the number 10 is always a rational number. Rational Numbers are the opposite of Irrational Numbers.

There two types of rational numbers:
  • A continuing decimal of a rational number always either terminates after a number of digits. For example 8 decimal digits - 98.37654506 .
  • begins to repeat the same limited sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. Example: 331.456456456456..... - repeating decimal numbers "456".
Rational numbers are all the numbers that can be expressed as fraction (proper or improper fraction - we will talk about fraction in detail later).
  • Any rational number can be expressed as integer divided by non-zero integer e.g integer/ non-zero integer. Example 4 = 4/1.
  • All "terminating" decimals are rational. Example 5.125 = 41/8.