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 nearest to 97-√, we can represent the number on a number line.
First, calculate the value of 97-√:
97-√ = 97 - 9.85 ≈ 87.15
Now, plot 87.15 on a number line by locating the whole numbers closest to it:
|___86______87____87.5___|___88______89____|
◄--87.15
The whole number nearest to 87.15 is 87, and the rational number nearest to 87.15 (to the nearest half) is 87.5.
To find the whole number and rational number to the nearest half for √97, we need to determine which two numbers on a number line surround √97.
Let's start by finding the perfect squares that are closest to 97. The perfect squares closest to 97 are 81 (9^2) and 100 (10^2).
Since 97 is between 81 and 100, its square root (√97) will be between the square roots of those two perfect squares.
Calculating the square roots of 81 and 100:
√81 = 9
√100 = 10
So, √97 is between 9 and 10 on the number line.
Now, let's find the number that is halfway between 9 and 10.
9 + 0.5 = 9.5
Therefore, the whole number and rational number to the nearest half that √97 is between are 9 and 9.5.