RATIONAL NUMBERS –
The numbers of the forms x/y, where ‘x’ & ‘y’ are integers and y ≠ 0 are called rational numbers.
Example.1) 6/17 is a rational numbers, since 6 & 17 are integers, and 17 ≠ 0
Example.2) 8/15 is a rational number, since 8 & 15 are integers, and 15 ≠ 0
Example.3) 121/125 is a rational numbers, since 121 & 125 are integers, and 125 ≠ 0
Example.4) 19/147 is a rational numbers, since 19 & 147 are integers, and 147 ≠ 0
Example.5) (-5)/17 is a rational number, since (-5) & 17 are integers, and 17 ≠ 0
Example.6) (-9)/41 is a rational number, since (-9) & 41 are integers, and 41 ≠ 0
Example.7) 7/(-27) is a rational number, since 7 & (-27) are integers, (-27) ≠ 0
Example.8) 19/(-121) is a rational numbers, since 19 & (-121) are integers, (-121) ≠ 0
Example.9) (-37)/(-149) is a rational numbers, since (-37) & (-149) are integers, and (-149) ≠ 0
Example.10) (-11)/(-79) is a rational numbers, since (-11) & (-79) are integers, and (-79) ≠ 0
We have already studied that every number of the form x/y, where ‘x’ & ‘y’ are integers and y ≠ 0 can always be expressed either as terminating decimal or as recurring decimal. In other words, every terminating as well as every repeating decimal is a rational numbers. Thus we have the following characteristics of rational number –
a) Every rational number is expressible either as a terminating decimal or as a repeating decimal.
b) Every terminating decimal is a rational number.
c) Every repeating decimal is a rational number.