What is #0.46# repeating as a fraction ?

2 Answers
Jim G.
Nov 12, 2017

#46/99#

Explanation:

#"create 2 equations with 0.46 repeating in both"#

#"let "x=0.bar(46)to(1)#

#"multiply both sides by "100#

#100x=46.bar(46)to(2)#

#"subtracting "(1)" from "(2)#

#100x-x=46.bar(46)-0.bar(46)#

#rArr99x=46#

#rArrx=46/99#

#rArr0.bar(46)=46/99#

George C.
Nov 12, 2017

#0.bar(46) = 46/99#

#0.4bar(6) = 7/15#

Explanation:

Case #bb(0.bar(46))#

If you intend #0.464646.... = 0.bar(46)# then:

#0.bar(46) = 46/99 * 0.bar(9) = 46/99 * 1 = 46/99#

Note that #46# and #99# have no common factors larger than #1#, so this is in simplest terms.

Case #bb(0.4bar(6))#

If you intend #0.4666... = 0.4bar(6)# then:

#0.4bar(6) = 0.bar(6) - 0.2#

#color(white)(0.4bar(6)) = 6/9*0.bar(9) - 0.2#

#color(white)(0.4bar(6)) = 6/9-1/5#

#color(white)(0.4bar(6)) = 2/3-1/5#

#color(white)(0.4bar(6)) = 10/15-3/15#

#color(white)(0.4bar(6)) = 7/15#

Note that #7# and #15# have no common factors larger than #1#, so this is in simplest terms.

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