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0o;;[o:RDoc::Markup::Paragraph;[I"HA rational number can be represented as a pair of integer numbers: ;TI"Ca/b (b>0), where a is the numerator and b is the denominator. ;TI"2Integer a equals rational a/1 mathematically.;To:RDoc::Markup::BlankLineo;;[I"HIn Ruby, you can create rational objects with the Kernel#Rational, ;TI"Dto_r, or rationalize methods or by suffixing +r+ to a literal. ;TI"5The return values will be irreducible fractions.;T@o:RDoc::Markup::Verbatim;[
I" Rational(1)      #=> (1/1)
;TI" Rational(2, 3)   #=> (2/3)
;TI"!Rational(4, -6)  #=> (-2/3)
;TI" 3.to_r           #=> (3/1)
;TI" 2/3r             #=> (2/3)
;T:@format0o;;[I"IYou can also create rational objects from floating-point numbers or ;TI"
strings.;T@o;
;[
I"?Rational(0.3)    #=> (5404319552844595/18014398509481984)
;TI"!Rational('0.3')  #=> (3/10)
;TI" Rational('2/3')  #=> (2/3)
;TI"
;TI"?0.3.to_r         #=> (5404319552844595/18014398509481984)
;TI"!'0.3'.to_r       #=> (3/10)
;TI" '2/3'.to_r       #=> (2/3)
;TI"!0.3.rationalize  #=> (3/10)
;T;0o;;[I"DA rational object is an exact number, which helps you to write ;TI"*programs without any rounding errors.;T@o;
;[I"K10.times.inject(0) {|t| t + 0.1 }              #=> 0.9999999999999999
;TI">10.times.inject(0) {|t| t + Rational('0.1') }  #=> (1/1)
;T;0o;;[I"PHowever, when an expression includes an inexact component (numerical value ;TI"6or operation), it will produce an inexact result.;T@o;
;[
I"#Rational(10) / 3   #=> (10/3)
;TI"/Rational(10) / 3.0 #=> 3.3333333333333335
;TI"
;TI"$Rational(-8) ** Rational(1, 3)
;TI"D                   #=> (1.0000000000000002+1.7320508075688772i);T;0;	I"rational.c;T;
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