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