Overline 075 as a Fraction
Have you ever come across the symbol "₀.075" and wondered what it means? This symbol is known as an overline, and it represents a repeating decimal. In this article, we will explore what the overline ₀.075 means and how to convert it to a fraction.
What is an Overline?
An overline is a horizontal line above a digit or a group of digits in a decimal number. It indicates that the digits under the line repeat indefinitely. For example, ₀.123 represents the decimal number 0.123123123..., where the digits 123 repeat indefinitely.
Converting Overline ₀.075 to a Fraction
To convert the overline ₀.075 to a fraction, we need to identify the repeating pattern. In this case, the repeating pattern is 075, which has three digits.
Let's multiply both sides of the equation by 1000 (since there are three digits in the repeating pattern):
1000x = 75.x
Now, subtract x from both sides:
999x = 75
Next, divide both sides by 999:
x = 75/999
Simplify the fraction:
x = 25/333
So, the overline ₀.075 is equivalent to the fraction 25/333.
Conclusion
In conclusion, the overline ₀.075 represents a repeating decimal, which can be converted to a fraction using simple algebraic manipulations. By identifying the repeating pattern and using the correct multiplication and division, we can convert the overline to the fraction 25/333. This technique can be applied to any overline decimal to convert it to a fraction.
