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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