Using a number line, what whole number and rational number to the nearest half is 10−−√
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 $\boxed{\frac{3}{2}}$.
To find the whole number and rational number to the nearest half of √10 using a number line, follow these steps:
1. Start by drawing a number line with 0 in the middle and positive numbers increasing to the right.
2. Locate the square root of 10 (√10) on the number line. √10 is approximately equal to 3.16.
3. The whole number closest to √10 is 3. Find the point 3 on the number line.
4. To find the rational number to the nearest half, draw a half point between 3 and 4 on the number line. This point is located at 3.5.
Therefore, the whole number nearest to √10 is 3 and the rational number nearest to half is 3.5.