0.87 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal representation of a number that has a sequence of digits that repeats indefinitely. One such example is 0.87, which is a repeating decimal. But have you ever wondered what 0.87 repeating as a fraction is? In this article, we will explore the answer to this question.
What is a Repeating Decimal?
Before we dive into finding the fraction equivalent of 0.87 repeating, let's first understand what a repeating decimal is. A repeating decimal is a decimal representation of a number that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal because the sequence "1234" 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 = 0.87 (repeating)
Let x = 0.87 (repeating) be the number we want to convert to a fraction.
Step 2: Multiply x by 100
Multiply x by 100 to get rid of the decimal point:
100x = 87.87 (repeating)
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 87
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 87/99
Simplifying the Fraction
We can simplify the fraction 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 conclusion, we have successfully converted 0.87 repeating to a fraction, which is 29/33. This exercise demonstrates the importance of understanding decimal representations and their equivalent fractions in mathematics.
