To express the decimal 0.8333333333 as a fraction, we can recognize that it is a repeating decimal. This means that the digit ‘3’ repeats indefinitely.
We can set this decimal equal to a variable, say x:
x = 0.8333333333…
Next, we can multiply both sides of the equation by 10 to shift the decimal point one place to the right:
10x = 8.3333333333…
Now, we subtract the first equation from the second:
10x – x = 8.3333333333… – 0.8333333333…
This simplifies to:
9x = 7.5
Now, we can solve for x:
x = 7.5 / 9
Both the numerator and the denominator can be simplified by dividing by 1.5:
x = 5 / 6
Thus, the decimal 0.8333333333 can be expressed as the fraction 5/6.