# CLASS-9RATIONAL NUMBERS

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.