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-sqrt(2), we first need to determine which whole numbers and rational numbers would be on either side of this value.
Since sqrt(2) is approximately 1.414, we know that 10-sqrt(2) is less than 10-1.414, which is approximately 8.586.
Now, let's consider the number line:
... 7.5 | 8.0 | 8.5 | 9.0 | 9.5 | 10.0 | 10.5 | ...
We can see that the nearest whole number to 10-sqrt(2) is 9, as it is closest to 8.586.
To find the nearest rational number to the nearest half, we look at the numbers 9 and 10 on the number line.
9 is closer to 8.5 than it is to 9.0, so the nearest rational number to the nearest half is 8.5.
Therefore, the whole number and rational number to the nearest half that is closest to 10-sqrt(2) are 9 and 8.5, respectively.
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 is closest to 97-sqrt(2), we first need to determine which whole numbers and rational numbers would be on either side of this value.
Since sqrt(2) is approximately 1.414, we know that 97-sqrt(2) is less than 97-1.414, which is approximately 95.586.
Let's consider the number line:
... 95.5 | 96.0 | 96.5 | 97.0 | 97.5 | 98.0 | 98.5 | ...
We can see that the nearest whole number to 97-sqrt(2) is 97, as it is closest to 95.586.
To find the nearest rational number to the nearest half, we look at the numbers 96.5 and 97 on the number line.
97 is closer to 97.0 than it is to 97.5, so the nearest rational number to the nearest half is 97.0.
Therefore, the whole number and rational number to the nearest half that is closest to 97-sqrt(2) are 97 and 97.0, respectively.
To find the whole number and rational number to the nearest half between 10 and √2, we can subtract √2 from 10 and then divide the result by 2.
1. Subtract √2 from 10:
10 - √2 ≈ 7.071
2. Divide the result by 2:
7.071 / 2 ≈ 3.536
Therefore, the whole number to the nearest half between 10 and √2 is 3, and the rational number to the nearest half is 3.5.