Recurring decimal into Fraction?

An alternate way is to use the concept of geometric series

0.318181818...
= 3/10 + 18/1000 + 18/100000 + .....
= 3/10 + (18/1000) / (1 - 1/100)
= 3/10 + (18/1000) / (99/100)
= 3/10 + 18/990
= 3/10 + 1/55
= (33 + 2)/110
= 35/110
= 7/22

change 0.3181818181818 into a fraction

let x = 0.3181818181818

1000x = 318.1818181818 [1]
10x = 3.181818181818 [2]

subtract [2] from [1]
990x = 315
x = 315/990
x = 7/22







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Well the idea here is simple

First step:

Multiply the number (Recurring decimal) by two number which only leaves the recurring decimal after the decimal.

Example 318.1818181818... multiplied by 1000 and 3.181818181818... multiplied by 10

Second step:

Subtract the two numbers, this causes the recurring part to disappear

Example: 318.1818181818.. - 3.181818181818... = 315

Third step:

Notice that this is 1000 (0.3181818181818...) - 10(0.3181818181818)

= 990 (0.3181818181818...)

Thus 990 (0.3181818181818...) = 315

OR 0.3181818181818... = 315/990 = (7 * 45 ) / ( 22 * 45) = 7/22

Do the branch. as an occasion evaluate a million/3. 3 (divide into) a million.00000=.333333 a repeating decimal. yet in any different case is with a calculator; enter 3 and press the a million/x button. this isn't any longer basic to instruct a thank you to accomplish a little those solutions via loss of the right symbols

x = 0.31818...

100x = 31.81818...
100x - x = 31.81818... - 0.31818...
99x = 31.5
x = 31.5/99
x = 315/990
x = (315/45)/(990/45)
x = 7/22

∴ 0.31818... = 7/22

Let x = 0.3181818181818
10x = 3.181818
1000x = 318.181818
990x = 315

x = 315/990, simplify -> 7/22