Using a number line, what whole number and rational number to the nearest half is √ 10 between?
To determine the whole number and rational number to the nearest half that √10 lies between, we need to locate √10 on a number line and identify the numbers to the left and right of it.
First, we can estimate the value of √10. Since 10 is between the perfect squares 9 and 16, we know that the square root of 10 lies between 3 and 4. To further narrow it down, we can approximate the value of √10 using a calculator:
√10 ≈ 3.1622.
On a number line, we can mark this value approximately between the whole numbers 3 and 4:
```
-----------------○-----○-----------------
3 √10 4
```
To find the whole number closest to √10, we can examine the distance from √10 to both whole numbers 3 and 4. We see that √10 is closer to 3 than to 4.
To find the rational number closest to √10 to the nearest half, we can look at the number line and determine the midpoint between 3 and 4:
```
-----------------○--●--○-----------------
3 3.5 √10 4
```
The rational number closest to √10 to the nearest half is 3.5.
Therefore, √10 lies between the whole number 3 and the rational number 3.5 to the nearest half.
Using a number line, what whole number and rational number to the nearest half is √ 97 between?
To determine the whole number and rational number to the nearest half that √97 lies between, we need to locate √97 on a number line and identify the numbers to the left and right of it.
√97 is an irrational number, so we need to estimate its value. Since 97 is between the perfect squares 81 and 100, we know that the square root of 97 lies between 9 and 10. To further narrow it down, we can approximate the value of √97 using a calculator:
√97 ≈ 9.8489.
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○-----------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we can examine the distance from √97 to both whole numbers 9 and 10. We see that √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we can look at the number line and determine the midpoint between 9 and 10:
```
---------------------○--------●--------○---------------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 10 and the rational number 9.5 to the nearest half.
wrong
Apologies for the confusion. Let's approach the problem again.
To find the whole number and rational number to the nearest half that √97 lies between, we first find the whole numbers that √97 is between.
Since 10^2 = 100 > 97 and 9^2 = 81 < 97, we know that √97 lies between 9 and 10.
Now, let's approximate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value between the whole numbers 9 and 10:
```
-------------------○----------------------------------------------------------○---------------
9 √97 10
```
To find the rational number closest to √97 to the nearest half, we can look at the number line and determine the midpoints between 9 and 10:
```
-------------------○-------------●-----------------------------------------○---------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
wrong answer
Apologies for the mistake. Let's attempt the problem again.
To find the whole number and rational number to the nearest half that √97 lies between, we can estimate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○-----------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we examine the distance from √97 to both whole numbers 9 and 10. √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we look at the number line and determine the midpoint between 9 and 10:
```
---------------------○-----------------------○---------------------
9 √97 10
```
The rational number closest to √97 to the nearest half is between 9 and 10, which is not a whole number or a rational number to the nearest half.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
Using a number line, what whole number and rational number to the nearest half is 97−−√ between?
To find the whole number and rational number to the nearest half that √97 lies between, we can estimate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○------------------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we examine the distance from √97 to both whole numbers 9 and 10. √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we look at the number line and determine the midpoint between 9 and 10:
```
---------------------○--------------●------------------○---------------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.