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

Answer 1

To find the whole number and rational number to the nearest half that is between $\sqrt{10}$, we need to consider the number line.

Let's represent $\sqrt{10}$ as a point on the number line. Since $\sqrt{10}\approx3.16$, we place it closer to 3 than to 4.

[asy]
unitsize(0.5cm);
int i;
for(i=-20; i<=51; ++i)
{
draw((i,-1)--(i,1));
label("$"+string(i)+"$", (i,-1.5), S);
}
draw((-2,0)--(6,0), linewidth(1.5));
dot((3,0), red);
[/asy]

To find the whole number to the nearest half, we look for the whole number that is closest to $\sqrt{10}$. In this case, the whole number closest to $\sqrt{10}$ is 3.

[asy]
unitsize(0.5cm);
int i;
for(i=-20; i<=51; ++i)
{
draw((i,-1)--(i,1));
label("$"+string(i)+"$", (i,-1.5), S);
}
draw((-2,0)--(6,0), linewidth(1.5));
dot((3,0), red);
label("$3$", (3,-1.5), S);
[/asy]

To find the rational number to the nearest half, we look for the multiple of $\frac{1}{2}$ that is closest to $\sqrt{10}$. In this case, the multiple of $\frac{1}{2}$ closest to $\sqrt{10}$ is $3\frac{1}{2}$.

[asy]
unitsize(0.5cm);
int i;
for(i=-20; i<=51; ++i)
{
draw((i,-1)--(i,1));
label("$"+string(i)+"$", (i,-1.5), S);
}
draw((-2,0)--(6,0), linewidth(1.5));
dot((3,0), red);
label("$3$", (3,-1.5), S);
dot((3.5,0), blue);
label("$3\frac{1}{2}$", (3.5,-1.5), S);
[/asy]

Thus, the whole number closest to $\sqrt{10}$ is $\boxed{3}$ and the rational number to the nearest half is $\boxed{3\frac{1}{2}}$.

Answer 2

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

Answer 3

To find the whole number and rational number to the nearest half that is between $\sqrt{10}$, we need to consider the number line.

Let's represent $\sqrt{10}$ as a point on the number line. Since $\sqrt{10}\approx3.16$, we place it closer to 3 than to 4.

[asy]
unitsize(0.5cm);
int i;
for(i=-20; i<=51; ++i)
{
draw((i,-1)--(i,1));
label("$"+string(i)+"$", (i,-1.5), S);
}
draw((-2,0)--(6,0), linewidth(1.5));
dot((3,0), red);
[/asy]

To find the whole number to the nearest half, we look for the whole number that is closest to $\sqrt{10}$. In this case, the whole number closest to $\sqrt{10}$ is 3.

[asy]
unitsize(0.5cm);
int i;
for(i=-20; i<=51; ++i)
{
draw((i,-1)--(i,1));
label("$"+string(i)+"$", (i,-1.5), S);
}
draw((-2,0)--(6,0), linewidth(1.5));
dot((3,0), red);
label("$3$", (3,-1.5), S);
[/asy]

To find the rational number to the nearest half, we look for the multiple of $\frac{1}{2}$ that is closest to $\sqrt{10}$. In this case, the multiple of $\frac{1}{2}$ closest to $\sqrt{10}$ is $3\frac{1}{2}$.

[asy]
unitsize(0.5cm);
int i;
for(i=-20; i<=51; ++i)
{
draw((i,-1)--(i,1));
label("$"+string(i)+"$", (i,-1.5), S);
}
draw((-2,0)--(6,0), linewidth(1.5));
dot((3,0), red);
label("$3$", (3,-1.5), S);
dot((3.5,0), blue);
label("$3\frac{1}{2}$", (3.5,-1.5), S);
[/asy]

Thus, the whole number closest to $\sqrt{10}$ is $\boxed{3}$ and the rational number to the nearest half is $\boxed{3\frac{1}{2}}$.