0.15 Repeating as a Fraction in Simplest Form
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.15 repeating, which can be written as 0.151515... . But have you ever wondered what this repeating decimal represents as a fraction in its simplest form?
Converting 0.15 Repeating to a Fraction
To convert a repeating decimal to a fraction, we can use a simple trick. Let's assume the repeating decimal is x. We can set up an equation by multiplying both sides by 100, since the decimal repeats every two digits.
100x = 15.15...
Now, subtract x from both sides to get:
99x = 15
Next, divide both sides by 99 to get:
x = 15/99
Simplifying the Fraction
The fraction 15/99 can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 15 and 99 is 3, so we can divide both numbers by 3:
x = (15 ÷ 3) / (99 ÷ 3) x = 5/33
And there you have it! The simplest form of 0.15 repeating as a fraction is 5/33.
Conclusion
In this article, we've seen how to convert a repeating decimal to a fraction in its simplest form. By using a simple trick and simplifying the fraction, we can find the equivalent fraction of a repeating decimal. In this case, the repeating decimal 0.15 is equal to the fraction 5/33.
