Its a recurring decimal
here are two other ways to solve the problem
1)
0.877777...
let x equal the decimal
x=0.877777...
multiply both sides by 10 because only one digit repeats
10x=8.7777...
subtract the first equation from the second new equation
10x=8.77777...
- x=0.87777...
9x=7.90000...
x=7.9/9
x=79/90
2)
0.877777...
multiply the decimal by 10 and then divide by 10
(10*0.877777...)/10
(8.77777...)/10
now you should realize that 0.77777....is equal to 7/9
(8 7/9)/10=(79/9)/10=79/90 again (9*8+7=79)
note: when one digit repeats, the fraction is that digit over 9
0.88888...=8/9, 0.444444...=4/9
when two digits repeat(without a lag), the fraction is the two digits over 99
0.36363636...=36/99=4/11
0.7272727272...=72/99=8/11
look for patterns in repeating decimals; they make your work easier
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