.888 Repeating as a Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is .888 repeating, which is a decimal that has the sequence "8" repeating infinitely. But have you ever wondered what this repeating decimal represents as a fraction?
The Fraction Representation
To find the fraction representation of .888 repeating, we can use the following steps:
Step 1: Let x = .888...
Let x be equal to .888 repeating. This means that x = .888888...
Step 2: Multiply x by 10
Multiply both sides of the equation by 10:
10x = 8.888...
Step 3: Subtract x from 10x
Subtract x from both sides of the equation:
10x - x = 8.888... - .888...
This simplifies to:
9x = 8
Step 4: Divide by 9
Divide both sides of the equation by 9:
x = 8/9
The Result
Therefore, .888 repeating as a fraction is equal to 8/9.
Conclusion
In conclusion, .888 repeating is equal to the fraction 8/9. This fraction representation provides an alternative way of expressing the repeating decimal, making it easier to understand and work with in mathematical calculations.
