Using a number line, what whole number and rational number to the nearest half is 10−−√ between?
To find the whole number and rational number to the nearest half that is closest to √10 on a number line, you can follow these steps:
1. Start by representing √10 on a number line. Place a point for √10 between two whole numbers to visually represent its approximate location.
2. Next, identify the whole number that is closest to √10. Compare the distance to √10 from each whole number on either side. Determine the whole number that has the shortest distance to √10.
3. Once you have identified the closest whole number, move half a unit to the right and half a unit to the left of that whole number on the number line. These two points represent the nearest rational numbers to the nearest half.
To make this process more concrete, let's go through each step:
1. Represent √10 on the number line:
-------------------------------------√10------------------------------------
2. Identify the whole numbers closest to √10. Let's say the whole number to the left of √10 is 3, and the whole number to the right is 4.
--------------3---√10---4---------------
3. Move half a unit to the right and half a unit to the left of the closest whole number:
--------------3---√10----3.5----4---------------
So, the whole number to the nearest half is 3, and the rational number to the nearest half which is closest to √10 is 3.5.
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 $\boxed{3\frac{1}{2}}$.
Using a number line, what whole number and rational number to the nearest half is 10−−√ between?
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 $\boxed{3\frac{1}{2}}$.
To determine the whole number and rational number that the square root of 10 is between to the nearest half on a number line, we can start by finding the two perfect squares closest to 10.
The perfect squares closest to 10 are 9 (3^2) and 16 (4^2).
Now, let's find the square root of 10 and its nearest half.
The square root of 10 lies between the square roots of 9 and 16.
√9 = 3 and √16 = 4.
To find the square root of 10, we can take the average of 3 and 4:
(3 + 4) / 2 = 7 / 2 = 3.5
So, the square root of 10 is approximately 3.5.
Therefore, the whole number and rational number to the nearest half that the square root of 10 lies between on a number line are 3 and 4.