0.87 Repeating as a Fraction
What is 0.87 Repeating?
0.87 repeating, also written as 0.87̄, is a repeating decimal. It is a decimal that has a sequence of digits that repeats indefinitely in a predictable pattern. In this case, the sequence "87" repeats indefinitely.
Converting 0.87 Repeating to a Fraction
To convert 0.87 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.87̄
Let x represent the repeating decimal 0.87̄.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 87.87̄
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
99x = 87
Step 4: Divide by 99
Divide both sides of the equation by 99 to get:
x = 87/99
Simplifying the Fraction
We can simplify the fraction 87/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 29/33
Therefore, 0.87 repeating as a fraction is 29/33.
Conclusion
In this article, we have successfully converted 0.87 repeating to a fraction, which is 29/33. This conversion is useful in many mathematical applications, such as algebra, geometry, and trigonometry.
