0.6222... as a Fraction
The Problem
You may have come across a repeating decimal like 0.6222... and wondered how to convert it into a fraction. This article will show you how to do just that.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In our case, the sequence is 22, which repeats indefinitely.
Converting 0.6222... to a Fraction
To convert a repeating decimal to a fraction, we need to use a few simple steps.
Step 1: Let x = 0.6222...
Let's assume that x = 0.6222...
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get rid of the decimal point. This gives us:
100x = 62.222...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to get:
99x = 61.6
Step 4: Divide by 99
Now, divide both sides of the equation by 99 to solve for x:
x = 61.6/99
x = 276/495
And there you have it! We've successfully converted 0.6222... to a fraction, which is 276/495.
Conclusion
Converting a repeating decimal to a fraction may seem daunting at first, but it's actually a simple process. By following the steps outlined above, you can convert any repeating decimal to a fraction. Remember to multiply by a power of 10 to get rid of the decimal point, subtract x from both sides, and then divide to solve for x. Happy calculating!
