Converting .3888 Repeating to a Fraction
.3888 repeating is a decimal number that has a pattern of 88 repeating indefinitely. In this article, we will explore how to convert this repeating decimal to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal because the sequence "1234" repeats indefinitely.
Converting .3888 Repeating to a Fraction
To convert .3888 repeating to a fraction, we can use the following steps:
Step 1: Let x = .3888 Repeating
Let's say x = .3888 repeating. This means that x = 0.38888888... (where the 88 pattern repeats indefinitely).
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 38.8888...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 38.5
Step 4: Solve for x
Now, divide both sides of the equation by 99 to solve for x:
x = 38.5 / 99
x = 44/99
Therefore, .3888 repeating as a fraction is equal to 44/99.
Simplifying the Fraction
We can simplify the fraction 44/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 44 and 99 is 11. Therefore, we can simplify the fraction as follows:
44/99 = 4/9
So, .3888 repeating as a fraction is equal to 4/9.
Conclusion
In conclusion, we have successfully converted .3888 repeating to a fraction, which is equal to 4/9. This article demonstrates the step-by-step process of converting a repeating decimal to a fraction.
