How Do You Turn a Repeating Decimal Into a Fraction?

The bar above the 4 means that it's a repeating decimal
Let the variable 'x' stand for the repeating decimal 0.4444...
Then we can form an equation, x=0.44444....
4 is the only repeating digit in our repeating decimal, which means we multiply both sides of our equation by 10
Remember, x=0.44444..., so we can put x instead of 0.44444...

1. Let the variable 'x' stand for the repeating decimal 0.44444...
2. Then we can form an equation, x=0.44444....
1. The number of repeating digits tells us how many zeros to put behind the 1
2. 4 is the only repeating digit in our repeating decimal, which means we multiply both sides of our equation by 10
3. If there were 2 repeating digits, like 0.424242..., we'd multiply by 100
4. If there were 3 repeating digits,0.425425..., we'd multiply by 1000
1. The Multiplication Property of Equality tells us that if we multiply one side of an equation by a number, we must also multiply the other side by that number
2. This allows us to multiply by numbers while still preserving the equality!
1. The number of repeating digits tells us how many zeros to put behind the 1
2. If there were 2 repeating digits, like 0.424242..., we'd multiply by 100
3. If there were 3 repeating digits,0.425425..., we'd multiply by 1000
1. The Subtraction Property of Equality says that if subtract a number from one side of an equation, we have to subtract it from the other
2. The bar above the 4 means that it's the repeating decimal 0.44444...
1. The bar above the 4 means that it's the repeating decimal 0.44444...
2. We're substituting x for 0.44444...
1. Let the variable 'x' stand for the repeating decimal 0.4444...
1. If any two things are equal to the same third thing, then they are all equal to each other!
2. The variable 'x' stands for the repeating decimal 0.4444...

Write the repeating decimal 0.4444444... as a fraction.