Write the percent as a fraction in simplest form. 83% =
The Correct Answer and Explanation is:
To convert a percentage to a fraction, you can follow a straightforward process. In this case, we will convert 83% into a fraction and simplify it to its lowest terms.
- Understanding the Percentage:
A percentage is essentially a fraction out of 100. Therefore, 83% can be expressed as:
[
\frac{83}{100}
] - Simplifying the Fraction:
The next step is to check if the fraction (\frac{83}{100}) can be simplified. Simplification involves finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
- Finding the GCD:
The number 83 is a prime number, which means its only divisors are 1 and 83. The number 100 can be factored into its prime components: (100 = 2^2 \times 5^2). Since 83 shares no common factors with 100 other than 1, the GCD of 83 and 100 is 1.
- Final Fraction:
Since the GCD is 1, we cannot simplify the fraction any further. Therefore, the fraction representation of 83% in its simplest form is:
[
\frac{83}{100}
] - Conclusion:
In summary, converting a percentage to a fraction involves expressing the percentage as a fraction with a denominator of 100. By determining the GCD, we can simplify the fraction. In this case, since 83 is a prime number and shares no common factors with 100 other than 1, (\frac{83}{100}) remains in its simplest form. Thus, the answer is:
[
83\% = \frac{83}{100}
]
This process highlights the relationship between percentages and fractions, showcasing how to convert and simplify them efficiently.