Using a number line what whole number and rational number to the nearest half is √ 107 between
Between 9.5 and 10
Between 10.5 and 11
Between 10 and 10.5
Between 11 and 11.5
To find a whole number and rational number to the nearest half that √107 is between, we can square different numbers until we find a square that is close to 107.
Let's start with the first given range, between 9.5 and 10:
9.5^2 = 90.25
10^2 = 100
Since 107 is between these two squares, we know that the square root of 107 (√107) is between 9.5 and 10.
Therefore, the whole number to the nearest half is 10.
Between 10.5 and 11:
10.5^2 = 110.25
11^2 = 121
Since 107 is between these two squares, √107 is between 10.5 and 11.
Therefore, the whole number to the nearest half is 11.
Between 10 and 10.5:
10^2 = 100
10.5^2 = 110.25
Since 107 is between these two squares, √107 is between 10 and 10.5.
Therefore, the whole number to the nearest half is 10.
Between 11 and 11.5:
11^2 = 121
11.5^2 = 132.25
Since 107 is between these two squares, √107 is between 11 and 11.5.
Therefore, the whole number to the nearest half is 11.
In summary:
√107 is between:
- 9.5 and 10, so the whole number to the nearest half is 10.
- 10.5 and 11, so the whole number to the nearest half is 11.
- 10 and 10.5, so the whole number to the nearest half is 10.
- 11 and 11.5, so the whole number to the nearest half is 11.
Answer is
√107 is between 10 and 10.5 on the number line. Therefore, the whole number to the nearest half is 10 and the rational number to the nearest half is 10.5.
To find the whole number and rational number to the nearest half for √107, we will compare the squared values of the given numbers to see which interval √107 falls into.
First, we will square the lower value of each interval:
- For 9.5, the squared value is 9.5^2 = 90.25.
- For 10.5, the squared value is 10.5^2 = 110.25.
- For 10, the squared value is 10^2 = 100.
- For 11, the squared value is 11^2 = 121.
Since the squared value of 107 is between 100 and 110.25, we know that √107 falls between 10 and 10.5.
To find the whole number and rational number to the nearest half, we will examine the two options:
1. Between 10 and 10.5: The rational number to the nearest half is 10.5, and the whole number is 10.
2. Between 9.5 and 10: The rational number to the nearest half is 10, and the whole number is also 10.
Therefore, the whole number and rational number to the nearest half for √107 is 10.