Using a number line, what whole number and rational number to the nearest half is √40 between?
To determine the whole number and rational number closest to √40, we first need to approximate the value of √40. The square root of 40 is approximately 6.32.
Now, let's consider the nearest whole number:
5 is less than 6.32, and 6 is greater than 6.32. Therefore, the whole number closest to √40 is 6.
Next, let's consider the nearest half:
To find the nearest half, we compare √40 to the values halfway between consecutive whole numbers. In this case, the halfway point between 6 and 7 is 6.5. Since 6.32 is closer to 6.5 than it is to 6, the rational number closest to √40 is 6.5.
Thus, √40 is between 6 and 6.5 on a number line.
using a number line what whole number and rational number to the nearest half is √67 in between?
To find the whole number and rational number to the nearest half that √40 is between, let's first find the value of √40:
√40 ≈ 6.324555320336759
The whole number to the nearest half that √40 is between is:
6 (on the left side)
The rational number to the nearest half that √40 is between is:
6.5 (on the right side)
So, √40 is between the whole number 6 and the rational number 6.5 on a number line.
To determine the closest whole number and rational number to the nearest half that √40 lies between on a number line, we can follow these steps:
Step 1: Find the integer values that the square root of 40 lies between.
We know that the square root of 40 is between 6 and 7 since:
√36 = 6
√49 = 7
So, √40 lies between these two whole numbers.
Step 2: Find the rational number to the nearest half between these whole numbers.
To find the rational number to the nearest half, we need to calculate the midpoint between the two whole numbers that √40 lies between.
The midpoint between 6 and 7 is calculated as:
(6 + 7) / 2 = 13 / 2 = 6.5
Therefore, the rational number to the nearest half that √40 lies between is 6.5.
In summary, the whole number to the nearest half that √40 lies between is 6, and the rational number to the nearest half is 6.5.