Square percentage
What percentage of the integers between 1 and 10,000 are square numbers?
Age
11 to 14
Challenge level
Problem
What percentage of the integers $1$, $2$, $3$, ... $9999$, $10000$ are square numbers?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 1%
Since $10,000 = 100^2$, the squares $1^2$, $2^2$, ... $99^2$, $100^2$ are all those between $1$ and $10000$. This means there are $100$ squares out of $10000$ numbers, so:
$\frac{100}{10000} = \frac{1}{100} = 1\%$
of the numbers are square numbers.