Repeating Decimal to Fraction
Note: "..." is the repeating sign I'm using.
Answer: 2/9
Steps
Let X equal the decimal number
Equation 1:
X = 0.2...
With 1 digit in the repeating decimal group,
create a second equation by multiplying
both sides by 10
X * 10 = 10X and 0.2...* 10 = 2.2...
Equation 2:
10X = 2.2...
Subtract equation 1 from equation 2
10X = 2.2... - X = 0.2...
We get
9X = 2
In conclusion, 0.2... = 2/9
Repeating Decimal to Mixed Number
This decimal cannot be a mixed number because it has no number in the one's, ten's, or hundred's place.