how to write 0.877777777 as a fraction

Question

Its a recurring decimal 

Answer 1

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

 

Answer 2

n = 0.87 where underline means repeat forever.

. .10n = 8.77

. . -n = -0.87

10n-n = 7.9

9n = 7.9

n = 7.9/9 = 79/90

Answer 3

Let's put it this way. The repeated part can be written as

 

            7/100 + 7/1000 + ........ = (7/100)[1+ (1/10) +(1/10²) + (1/10³)......]

 

What we have in square brakets is a sum of geometric series which is equal to

 

                             1/(1-1/10) = 10/9

Thus your number is

 

         0.87777... = (8/10) +(7/100)(10/9) = (8/10) + (7/90) =79/90

Answer 4

Let x=.8777777.... (equation 1)

 

Multiply both the sides by 10

 

10x=8.777777..... (equation 2)

 

subtract the equation 1 from equation 2

 

10x=8.777777.....

   x=  .877777.....

-

—————————

 9x=7.900000...

 

 9x=7.9

 

divide both the sides by 9

 

9x/9=7.9/9

 

x=7.9/9

 

x=79/90

Answer 5

Let .8[7] be defined as .8777.... where SQUARE brackets are used to denote repeating quantities

 

.8[7]= .8 + [.07] = .8 + [.7]/10

 

Let x= [.7]

 

10x= 7 + x    <----think about that for awhile (it's a recursion relation)

 

x=7/9

 

Now we have all we need

 

.8[7]=8/10+(7/9)/10 = (8+ 7/9)/10 = 79/90

Answer 6

87 =

99

 

 

write   8 and repeated pattern 7 on top ( numerator) , and 9's equal to number of digits at the bottom

denominator.

 

  Like   : 1/ 6 = 0. 1666666

                

           1/6 = 16 /99

             16 * 6 = 69