Answer:
Step-by-step explanation: First, create an equation that represents the repeating decimal that you want to convert to a fraction
x = 2.267267.... (1)
There are 3 repeating decimals, multiply both sides of the equation by 103 = 1000 so that both equations have the same repeating digits to the right of the decimal point
1000x = 2267.267267... (2)
Subtract the equation (1) from equation (2)
1000x
x =
= 2267.267267...
2.267267...
999x = 2265
Solve for the x in the equation to determine the equivalent fraction.
x =
2265
999
Since the greatest common factor of 2265 and 999 is 3, we can simplify the fraction and show the same amount
2265
999
=
2265 ÷ 3
999 ÷ 3
=
755
333
Therefore, 755/333 is simplified fraction of 2.267 repeating. Since this is an improper fraction, converted to mixed number is:
755
333
= 2
89
333
Therefore, 2.267 repeating as a fraction is 755/333 and It is written as 2 89/333 in mixed number form.