Write 2.8% as a fraction in simplest form.
The Correct Answer and Explanation is:
To write 2.8% as a fraction in simplest form:
- Convert the percentage to a fraction:
Percent means “per 100,” so 2.8% is written as:
[
\frac{2.8}{100}
] - Eliminate the decimal:
To remove the decimal from the numerator, multiply both the numerator and denominator by 10:
[
\frac{2.8 \times 10}{100 \times 10} = \frac{28}{1000}
] - Simplify the fraction:
Find the greatest common divisor (GCD) of 28 and 1000, which is 4. Divide both the numerator and denominator by 4:
[
\frac{28 \div 4}{1000 \div 4} = \frac{7}{250}
]
Thus, 2.8% as a fraction in simplest form is ( \frac{7}{250} ).
Detailed Explanation:
Converting percentages into fractions involves understanding the relationship between percentages and fractions. A percentage represents parts per 100. For example, 50% means ( \frac{50}{100} ), which simplifies to ( \frac{1}{2} ). Similarly, 2.8% means ( \frac{2.8}{100} ). However, because the numerator (2.8) is a decimal, it needs to be converted to a whole number to work with fractions more easily.
To eliminate the decimal, multiply both the numerator and denominator by 10 (or a higher power of 10, depending on the number of decimal places). This shifts the decimal point to the right, making the numerator a whole number.
Once the fraction is obtained with whole numbers, simplifying it is crucial. Simplification involves dividing both the numerator and denominator by their greatest common divisor (GCD), which ensures the fraction is in its simplest form. For ( \frac{28}{1000} ), the GCD is 4, resulting in ( \frac{7}{250} ).
This final fraction, ( \frac{7}{250} ), is the simplest form because 7 and 250 share no common factors other than 1. This process ensures clarity and precision when representing percentages as fractions.