0.23 Repeating As A Fraction, Have you ever encountered the decimal number 0.23 repeating? It's a peculiar decimal that seems to, General, 0-23-repeating-as-a-fraction, JPOSE
Have you ever encountered the decimal number 0.23 repeating? It's a peculiar decimal that seems to go on forever without any pattern. But did you know that this decimal can be expressed as a fraction?
To understand how to convert 0.23 repeating to a fraction, we first need to understand what repeating decimals are. A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. In the case of 0.23 repeating, the pattern is simply "23" repeating indefinitely.
To convert 0.23 repeating to a fraction, we'll use a trick that involves multiplying both sides of the equation by a power of 10. Let's call our repeating decimal "x" for simplicity's sake. We'll start by multiplying both sides of the equation by 100, which is 10 to the power of 2:
100x = 23.232323...
Now, we'll subtract the original equation from this new equation:
100x - x = 23.232323... - 0.232323...
Simplifying the right side gives us:
99x = 23
Dividing both sides by 99 gives us our final answer:
x = 23/99
Therefore, 0.23 repeating can be expressed as the fraction 23/99.
It's worth noting that this method works for any repeating decimal, not just 0.23 repeating. By multiplying both sides of the equation by an appropriate power of 10, we can eliminate the repeating pattern and solve for the fraction.
In conclusion, 0.23 repeating can be expressed as the fraction 23/99. Knowing how to convert repeating decimals to fractions is a useful trick that can come in handy in various mathematical contexts.