0.03 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal like 0.03 to a fraction? In this article, we'll explore the steps to convert 0.03 repeating to a fraction.
What is 0.03 Repeating?
0.03 repeating, also written as 0.030303..., is a decimal number that has a repeating pattern of 03. This pattern continues indefinitely, making it a non-terminating decimal.
Converting 0.03 Repeating to a Fraction
To convert 0.03 repeating to a fraction, we can use a simple trick. Let's multiply the decimal by 100, which is the same as shifting the decimal point two places to the right. This gives us:
100x = 3.030303...
Now, subtract the original decimal from the new equation:
100x - x = 3.030303... - 0.030303... 99x = 3
Next, divide both sides by 99:
x = 3/99
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 3 and 99 is 3, so we can simplify the fraction as follows:
x = 1/33
And there you have it! The repeating decimal 0.03 is equal to the fraction 1/33.
Conclusion
In this article, we've seen how to convert a repeating decimal like 0.03 to a fraction using a simple trick. By multiplying by 100, subtracting the original decimal, and simplifying the resulting fraction, we can convert 0.03 repeating to the fraction 1/33.
