6.75% [tex]\Rightarrow \frac{75}{100}[/tex]
Answer (2)
Convert the percentage 6.75% to a decimal: 6.75% = 100 6.75 = 0.0675 .
Convert the decimal 0.0675 to a fraction: 0.0675 = 10000 675 .
Simplify the fraction 10000 675 by dividing both the numerator and the denominator by their GCD, which is 25: 10000 ÷ 25 675 ÷ 25 = 400 27 .
The correct representation of 6.75% as a fraction is 400 27 .
Explanation
Problem Analysis The problem provides a percentage, 6.75%, and states that it is equivalent to the fraction 100 75 . We need to analyze this statement to determine if it's correct and, if not, find the correct representation of the percentage as a fraction.
Converting Percentage to Decimal First, let's convert the percentage 6.75% to a decimal by dividing by 100: 6.75% = 100 6.75 = 0.0675
Converting Decimal to Fraction Now, let's convert the decimal 0.0675 to a fraction. To do this, we can write it as a fraction with a denominator of 10000 (since there are four decimal places): 0.0675 = 10000 675
Simplifying the Fraction Next, we simplify the fraction 10000 675 by finding the greatest common divisor (GCD) of 675 and 10000. We can divide both the numerator and the denominator by their GCD.
Dividing by GCD The GCD of 675 and 10000 is 25. Dividing both the numerator and the denominator by 25, we get: 10000 ÷ 25 675 ÷ 25 = 400 27
Comparing and Concluding The given fraction is 100 75 , which simplifies to 4 3 or 0.75. This is not equal to 6.75%. Therefore, the initial statement is incorrect. The correct representation of 6.75% as a fraction is 400 27 .
Final Answer Therefore, 6.75% is equal to 400 27 , not 100 75 .
Examples
In financial calculations, percentages are often converted to fractions or decimals to calculate interest, taxes, or discounts. For example, if you want to calculate the sales tax on an item that costs $100 and the sales tax rate is 6.75%, you would convert 6.75% to a decimal (0.0675) and multiply it by the cost of the item: $100 * 0.0675 = $6.75. This gives you the amount of sales tax you need to pay. Incorrectly converting the percentage could lead to significant errors in financial calculations. Understanding how to accurately convert percentages to fractions and decimals is crucial for making informed financial decisions.
6.75% is correctly converted to the fraction 400 27 . The initial statement claiming it equals 100 75 is incorrect. Thus, accurate conversion is essential for understanding percentage values.
;
