If you answered 40 problems correctly on a 42-question test, what percent of the problems did you answer correctly?
The Correct Answer and Explanation is:
To calculate the percentage of problems answered correctly, you use the formula:Percentage=(Number of correct answersTotal number of questions)×100\text{Percentage} = \left( \frac{\text{Number of correct answers}}{\text{Total number of questions}} \right) \times 100Percentage=(Total number of questionsNumber of correct answers)×100
In this case:
- The number of correct answers is 40.
- The total number of questions is 42.
Now, substitute these values into the formula:Percentage=(4042)×100\text{Percentage} = \left( \frac{40}{42} \right) \times 100Percentage=(4240)×100
First, divide 40 by 42:4042=0.9524\frac{40}{42} = 0.95244240=0.9524
Then, multiply by 100 to convert it into a percentage:0.9524×100=95.240.9524 \times 100 = 95.240.9524×100=95.24
Therefore, you answered 95.24% of the questions correctly.
Explanation:
The formula used above is a straightforward method to calculate percentages. You divide the part (correct answers) by the whole (total questions) and multiply the result by 100 to convert it into a percentage. This allows you to express your performance as a percentage of the total possible score.
A 95.24% score is an excellent result, indicating that you answered the vast majority of the questions correctly. This can be interpreted as almost perfect performance, showing a strong understanding of the material tested.
