Find the percentage of numbers which are multiples of 5 from the set {1, 2, 3, 4, ..., up to 52}. Write the answer correct to one decimal place.

Steps to Solve

1. Find the number of multiples of 5 in the set To find the number of multiples of 5 in the set {1, 2, 3, ..., 52}, we need to find the largest multiple of 5 that is less than or equal to 52. This is $5 \times 10 = 50$. Since $5 \times 1 = 5$ is the smallest multiple of 5 in the set, we have the multiples 5, 10, 15, ..., 50. These are $5 \times 1, 5 \times 2, 5 \times 3, ..., 5 \times 10$, so there are 10 multiples of 5. Alternatively, we can divide 52 by 5 and take the integer part of the result: $\lfloor \frac{52}{5} \rfloor = 10$.

2. Calculate the percentage of multiples of 5 The percentage of multiples of 5 is the number of multiples of 5 divided by the total number of elements in the set, multiplied by 100. $$ \frac{10}{52} \times 100 $$

3. Simplify the fraction and calculate the percentage $$ \frac{10}{52} \times 100 = \frac{1000}{52} = \frac{250}{13} \approx 19.230769 $$

4. Round to one decimal place Rounding 19.230769 to one decimal place gives 19.2.