.84 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to convert .84 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, .84 repeating is a repeating decimal because the sequence "84" repeats indefinitely.
Converting .84 Repeating into a Fraction
To convert .84 repeating into a fraction, we can use the following steps:
Step 1: Let x = .84 Repeating
Let's start by letting x = .84 repeating.
Step 2: Multiply x by 100
Next, we'll multiply x by 100 to get rid of the decimal point.
100x = 84.84
Step 3: Subtract x from 100x
Now, we'll subtract x from 100x to get:
99x = 84
Step 4: Solve for x
Finally, we'll solve for x by dividing both sides of the equation by 99.
x = 84/99
x = 42/49
And that's it! We've successfully converted .84 repeating into a fraction, which is 42/49.
Conclusion
Converting a repeating decimal into a fraction is a simple process that requires a few basic algebraic steps. By following these steps, we can convert any repeating decimal into a fraction. In this case, we converted .84 repeating into the fraction 42/49.
