fractions, decimals, and percents

Question

How to make 22.2%(repeating) a decimal, and fraction

Answer 1

22.222...%

to change the percent to a decimal, move the decimal point 2 places to the left

0.22222... is the decimal

 

let n=0.222222...

multiply both sides by 10 because there is only 1 digit in the repetend

10n=2.222222...

now subtract the first equation from the second equation

10n=2.222222...

-

   n=0.222222...

________________

 9n=2 because the decimal parts get eliminated (2-2=0 for all the 2s)

   n=2/9 is the fraction

whenever you have a repeating decimal and there is no lag, simply put the repetend over 9, or 99, or 999, and so on depending on how many digits are in the repetend

for example:

0.363636...=36/99=4/11

0.6666...=6/9=2/3

0.459459459...=459/999=51/111=17/37

0.714285714285714285...=714285/999999=79365/111111=26455/37037=715/1001=65/91=5/7