What is #0.46# repeating as a fraction ?
2 Answers
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#
Explanation:
Case
If you intend
#0.bar(46) = 46/99 * 0.bar(9) = 46/99 * 1 = 46/99#
Note that
Case
If you intend
#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