Converting .206 to a Fraction
In mathematics, converting a decimal to a fraction is a fundamental concept that involves expressing a decimal value as a ratio of two integers. In this article, we will explore how to convert the decimal value .206 to a fraction.
What is .206?
.206 is a decimal value that represents a fraction of a whole. In everyday life, we often encounter decimal values in various contexts, such as measurements, percentages, and ratios.
Converting .206 to a Fraction
To convert .206 to a fraction, we need to find the numerator and denominator of the fraction. The numerator represents the number of equal parts, and the denominator represents the total number of parts.
To convert .206 to a fraction, we can follow these steps:
- Divide .206 by 1, which gives us:
.206 ÷ 1 = .206
Step 2: Find the Least Common Multiple (LCM)
To find the LCM, we need to multiply the numerator and denominator by a common multiple that will eliminate the decimal point.
In this case, the LCM is 1000. Therefore, we multiply both the numerator and denominator by 1000:
(.206 × 1000) / (1 × 1000) = 206 / 1000
Simplifying the Fraction
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 206 and 1000 is 2. Therefore, we divide both the numerator and denominator by 2:
(206 ÷ 2) / (1000 ÷ 2) = 103 / 500
The Final Answer
The final answer is:
.206 = 103/500
Conclusion
In conclusion, converting .206 to a fraction involves dividing the decimal value by 1, finding the LCM, and simplifying the fraction by dividing both the numerator and denominator by their GCD. By following these steps, we can convert .206 to the fraction 103/500. This conversion is essential in various mathematical applications, such as algebra, geometry, and calculus.
