Using a number line what whole number and rational number to the nearest half is ✓105 between?
The decimal representation of √105 is approximately 10.246211.
On a number line, the whole number and rational number to the nearest half that √105 is between can be determined by finding the whole number and rational number that are closest to 10.246211.
To find the whole number closest to 10.246211, we round it to the nearest whole number, which is 10.
To find the rational number to the nearest half, we round it to the nearest multiple of 0.5. Since 10.246211 is closer to 10, we round it to the nearest half below 10, which is 10 - 0.5 = 9.5.
Therefore, √105 is between the whole number 10 and the rational number 9.5 on a number line.
To find the whole number and rational number to the nearest half that ✓105 is between, we can start by locating ✓105 on a number line.
The nearest whole number to ✓105 is 11, as 10² = 100 and 11² = 121. So, we know that ✓105 is greater than 10 and less than 11.
Now, let's find the nearest half. To do this, we can split the interval between 10 and 11 into halves.
The halfway point between 10 and 11 is 10.5. Since ✓105 is greater than 10.5, we know it is closer to 11.
Therefore, the whole number to the nearest half that ✓105 is between is 11. Additionally, ✓105 itself is a rational number, so the rational number to the nearest half that ✓105 is between is also 11.