.333 Repeating as a Fraction
The repeating decimal .333 is a common occurrence in mathematics, but have you ever wondered what it represents as a fraction? In this article, we'll dive into the world of decimal expansions and explore how to convert .333 repeating into a simple fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of .333, the sequence "3" repeats forever. This type of decimal is also known as a non-terminating, repeating decimal.
Converting .333 Repeating to a Fraction
To convert .333 repeating to a fraction, we can use a simple trick. Let's multiply .333 by 10 to get:
10 × .333 = 3.333
Now, subtract the original value from the new value:
3.333 - .333 = 3
This leaves us with:
.333 = 1/3
Voilà! We've converted .333 repeating to a simple fraction: one-third.
Why Does This Work?
The reason this trick works is due to the nature of repeating decimals. When we multiply .333 by 10, we're essentially "shifting" the decimal point one place to the right. This creates a new sequence of digits that repeats indefinitely, but with an additional digit. By subtracting the original value, we're left with a whole number, which represents the fraction.
Other Examples
This trick can be applied to any repeating decimal. For example, let's convert .666 repeating to a fraction:
10 × .666 = 6.666 6.666 - .666 = 6 .666 = 2/3
Similarly, we can convert .999 repeating to a fraction:
10 × .999 = 9.999 9.999 - .999 = 9 .999 = 9/9 = 1
Conclusion
In conclusion, converting .333 repeating to a fraction is a simple process that involves multiplying by 10 and subtracting the original value. This trick can be applied to any repeating decimal, making it a useful tool in mathematics. Whether you're a student or a math enthusiast, understanding how to work with repeating decimals can open up new doors to mathematical exploration and discovery.
