Question #c4442
2 Answers
Let x equal the number.
Use multiples of powers of 10 to write 2 equations that allow you to subtract away the repeating part.
Solve the remaining equation.
Explanation:
Please notice that the bar over the 2 indicates an infinite repetition.
let
Multiply by both 10, because that leave only the repetitive part to the right of the decimal and mark as equation [1]:
Multiply equation [1] by 10, because that will move 1 repetition to the left of the decimal and mark as equation [2]:
Subtract equation [1] from equation [2]:
Please observe that the infinite repeating 2s to the right of the decimal sum to 0:
Solve for x by dividing both sides by 90:
Reduce the fraction:
Check with a calculator:
This checks.
Explanation:
#"we have "0.0bar(2)#
#"where "0.0bar(2)-=0.02222....#
#"we require to create equations with only the repeated"#
#"digit appearing after the decimal point"#
#"let "x=0.0bar(2)#
#"then "10x=0.bar(2)to(1)#
#"and "100x=2.bar(2)to(2)#
#"subtracting "(1)" from "(2)" eliminates "bar(2)#
#rArr100x-10x=2.bar(2)-0.bar(2)#
#rArr90x=2#
#rArrx=2/90=1/45larrcolor(blue)"in simplest form"#
#rArr0.0bar(2)-=1/45#