LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RATIONAL 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.**