0.84 Recurring as a Fraction
What is 0.84 Recurring?
0.84 recurring, also written as 0.84..., is a non-terminating decimal that has a repeating pattern of digits. In this case, the pattern is "84" which repeats indefinitely.
Converting 0.84 Recurring to a Fraction
To convert 0.84 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.84...
Let's assume that x = 0.84...
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get:
100x = 84.84...
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 84
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 84/99
Simplifying the Fraction
We can simplify the fraction 84/99 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3.
x = 84/99 = 28/33
Therefore, 0.84 recurring as a fraction is equal to 28/33.
Conclusion
In conclusion, we have successfully converted 0.84 recurring to a fraction, which is equal to 28/33. This process can be applied to any non-terminating decimal to convert it into a simplified fraction.
