Express 89 percent as fraction in the simplest form
The Correct Answer and Explanation is :
The correct answer is: (\frac{89}{100})
To express 89 percent as a fraction in its simplest form, we start by understanding what “percent” means. The term “percent” comes from the Latin phrase “per centum,” which means “by the hundred.” Therefore, 89 percent can be written as:
[
89\% = \frac{89}{100}
]
This fraction indicates that 89 out of every 100 parts are being considered.
Next, we need to simplify this fraction, if possible. To do this, we check for any common factors between the numerator (89) and the denominator (100). The number 89 is a prime number, which means it only has two positive divisors: 1 and 89 itself.
Now, we list the prime factors of the denominator:
- The number 100 can be factored into (10 \times 10) or (2^2 \times 5^2). The prime factors of 100 are 2 and 5.
Since the numerator (89) does not share any common factors with the denominator (100), we conclude that (\frac{89}{100}) is already in its simplest form.
Thus, the fraction representing 89 percent in simplest form is:
[
\frac{89}{100}
]
In conclusion, converting a percentage to a fraction involves dividing the percentage by 100. The next step is simplifying the fraction by finding common factors, but in this case, 89 is prime and does not share factors with 100, resulting in (\frac{89}{100}) being in its simplest form. This process is fundamental in mathematics, especially when dealing with ratios, proportions, and comparisons, allowing for easier calculations and understanding of quantities in different contexts.