Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?
To determine which whole number and rational number to the nearest half is $\sqrt{105}$ between, we need to find the two closest numbers to $\sqrt{105}$ on a number line.
We know that $\sqrt{100}=10$ and $\sqrt{121}=11$.
Since $\sqrt{105}$ is closer to 10 than it is to 11, we can conclude that $\sqrt{105}$ is between the whole numbers 10 and 11 on the number line.
To find a rational number to the nearest half, we need to find a number halfway between 10 and 11. Adding $\frac{1}{2}$ to 10 gives us $10+\frac{1}{2}=\frac{20}{2}+\frac{1}{2}=\frac{21}{2}=\boxed{10.5}$.
To find the whole number and rational number nearest to √105 to the nearest half, we can start by finding the square root of 105.
√105 is approximately 10.246
To find the whole number nearest to √105, we round the decimal down to the nearest whole number. In this case, the whole number nearest to √105 is 10.
To find the rational number nearest to √105 to the nearest half, we need to determine whether the decimal part of √105 is closer to 0 or 0.5.
In this case, 0.246 is closer to 0 than 0.5.
So, the whole number and the rational number to the nearest half that √105 is between are:
Whole number: 10
Rational number: 10