Irrational and Real Numbers
Revision : Rational numbers
The numerators in the numbers , , , are integers while their denominators are non-zero integers. Hence, these are rational numbers. If p is any integer and q, any non-zero integer, then, is a rational number
The decimal form of a rational number
Two rational numbers can have different decimal forms. To understand the nature of this difference, let us work out the decimal form of two rational numbers and , and study them. What is the difference in the decimal forms ?
(1) The decimal form of .
The decimal form of is 7.9375
As the remainder in this example is 0, the process of division is complete. Hence, we do not get any digit after 5 in the quotient obtained.
It means that the decimal form 7.9375 is a terminating one.
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