To convert the mixed number 3 8 repeating (which is expressed as 3.888…) into a fraction, we can follow some simple steps.
First, let’s denote x as the repeating decimal:
- x = 3.888…
Next, we can separate the whole number from the decimal part:
- This can be rewritten as: x = 3 + 0.888…
Now, let’s focus on the decimal part, 0.888…. We can denote this part as y:
- y = 0.888…
To eliminate the repeating decimal, we can multiply y by 10:
- 10y = 8.888…
Now we have two equations:
- y = 0.888…
- 10y = 8.888…
If we subtract the first equation from the second:
- 10y – y = 8.888… – 0.888…
- This simplifies to: 9y = 8
By solving for y, we get:
- y = rac{8}{9}
Now, we can substitute this value back into our equation for x:
- x = 3 + rac{8}{9}
To combine these, we need a common denominator. We can express 3 as a fraction:
- 3 = rac{27}{9}
Now we can add the fractions:
- x = rac{27}{9} + rac{8}{9} = rac{35}{9}
Thus, the fraction that represents 3 8 repeating is rac{35}{9}.