0.8888 Repeating as a Fraction
Introduction
The repeating decimal 0.8888 is a type of decimal that has a pattern of digits that repeats indefinitely. In this article, we will explore how to convert 0.8888 into a fraction.
Converting 0.8888 to a Fraction
To convert 0.8888 to a fraction, we can use the following steps:
Step 1: Let x = 0.8888
Let's assume that x = 0.8888.
Step 2: Multiply Both Sides by 100
Since the repeating pattern in 0.8888 starts after the decimal point, we can multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 88.8888
Step 3: Subtract x from Both Sides
Now, we can subtract x from both sides of the equation to get:
99x = 88.8888 - 0.8888
99x = 88
Step 4: Divide Both Sides by 99
Finally, we can divide both sides of the equation by 99 to get:
x = 88/99
x = 8/9
Therefore, 0.8888 as a fraction is equal to 8/9.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.8888 to a fraction, which is 8/9. This exercise demonstrates how to convert a repeating decimal to a fraction using basic algebraic manipulations.
