Write $4.16 \%$ as a mixed number.
Answer (2)
Convert the percentage to a fraction: 4.16% = 100 4.16 .
Remove the decimal: 100 4.16 = 10000 416 .
Simplify the fraction by dividing by the GCD (16): 10000 416 = 625 26 .
Express as a mixed number: 625 26 .
Explanation
Converting Percentage to Fraction We are asked to express 4.16% as a mixed number. First, we need to convert the percentage to a fraction.
Removing Decimal To convert a percentage to a fraction, we divide by 100. So, we have 4.16% = 100 4.16 To remove the decimal in the numerator, we multiply both the numerator and the denominator by 100: 100 4.16 = 100 × 100 4.16 × 100 = 10000 416 .
Simplifying the Fraction Now, we need to simplify the fraction 10000 416 by finding the greatest common divisor (GCD) of 416 and 10000. The GCD of 416 and 10000 is 16. We divide both the numerator and the denominator by 16: 10000 416 = 10000 ÷ 16 416 ÷ 16 = 625 26 .
Expressing as a Mixed Number Since 26/625 is a proper fraction (the numerator is less than the denominator), the mixed number representation of 4.16% is simply 625 26 because the whole number part is 0.
Final Answer Therefore, 4.16% expressed as a mixed number is 625 26 .
Examples
Percentages are commonly used in everyday life, especially in financial calculations. For example, when calculating interest rates on loans or savings accounts, understanding how to convert percentages to fractions or mixed numbers is essential. If you have a loan with an annual interest rate of 4.16%, expressing this percentage as a fraction (26/625) can help you calculate the exact amount of interest you will pay over a certain period. This conversion allows for precise calculations and better financial planning.
To express 4.16% as a mixed number, we convert it into a fraction and simplify it. This results in 625 26 , which is a proper fraction and can be considered the mixed number itself. Therefore, the final answer is 625 26 .
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