Using a number line, what whole number and rational number to the nearest half is 10−−√

Answer 1

First, let's find the whole number nearest to $\sqrt{10}$. We know that $3^2=9$ and $4^2=16$, so $\sqrt{10}$ is between 3 and 4. Therefore, the whole number nearest to $\sqrt{10}$ is $\boxed{3}$.

Next, let's find the rational number to the nearest half. We know that $\sqrt{10}$ is between $\sqrt{9}=3$ and $\sqrt{16}=4$. Since the nearest multiples of $\frac{1}{2}$ to 3 and 4 are $\frac{3}{2}$ and $\frac{4}{2}=2$, respectively, the rational number to the nearest half is $\boxed{\frac{3}{2}}$.