3.2 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 3.2 repeating, which can be written as 3.232323... . But have you ever wondered how to express this repeating decimal as a fraction? In this article, we'll explore how to convert 3.2 repeating into a fraction.
The Concept of Repeating Decimals
Repeating decimals are a type of non-terminating decimal that has a sequence of digits that repeats over and over again. They can be identified by the presence of a bar or dot above the repeating digits. For example, 0.12341234... is a repeating decimal, where the sequence "1234" repeats indefinitely.
Converting 3.2 Repeating to a Fraction
To convert 3.2 repeating into a fraction, we need to use a simple trick. Let's start by assuming that the repeating decimal can be represented as:
x = 3.232323...
Next, we multiply both sides of the equation by 100, which gives us:
100x = 323.232323...
Now, subtract the original equation from the new equation:
100x - x = 323.232323... - 3.232323...
This simplifies to:
99x = 320
Finally, divide both sides by 99:
x = 320/99
So, 3.2 repeating can be expressed as a fraction: 320/99.
Conclusion
In conclusion, converting 3.2 repeating into a fraction involves a simple trick of multiplying and subtracting the equation. By using this method, we can express the repeating decimal as a fraction, which is 320/99. This concept can be applied to convert any repeating decimal into a fraction, making it an essential technique in mathematics.
