How do you you express 0.31111111111111 recurring as a common fraction?

Answer 1

To express 0.31111111111111 recurring as a common fraction, we can set x = 0.31111111111111 and then multiply x by 10 to shift the decimal point to the right, yielding 10x = 3.1111111111111. Next, we subtract the original equation from the shifted equation to eliminate the repeating decimal, giving 9x = 2.8. Finally, we divide both sides by 9 to solve for x, resulting in x = 2.8/9 = 28/90. Therefore, 0.31111111111111 recurring as a common fraction is 28/90.

Answer 2

Suppose f = 0.3111...

then 10f = 3.111....

Subtracting the second from the first, 9f = 2.8

so that f = 2.8/9 = 28/90 which simplifies to 14/45

Suppose f = 0.3111...

then 10f = 3.111....

Subtracting the second from the first, 9f = 2.8

so that f = 2.8/9 = 28/90 which simplifies to 14/45

Suppose f = 0.3111...

then 10f = 3.111....

Subtracting the second from the first, 9f = 2.8

so that f = 2.8/9 = 28/90 which simplifies to 14/45

Suppose f = 0.3111...

then 10f = 3.111....

Subtracting the second from the first, 9f = 2.8

so that f = 2.8/9 = 28/90 which simplifies to 14/45

Answer 3

Suppose f = 0.3111...

then 10f = 3.111....

Subtracting the second from the first, 9f = 2.8

so that f = 2.8/9 = 28/90 which simplifies to 14/45