Using a number line, what whole number and rational number to the nearest half is 97−−√ between?(1 point)
97−−√ is between and
wrong
I apologize for the mistake. Let's try again.
To find the whole number that 97−−√ is closest to, we can take the floor of the square root. The square root of 97 is approximately 9.84885780179. When rounded down, the whole number closest to 9.84885780179 is 9.
To find the rational number to the nearest half, we can compare the decimal part of the square root to 0.5. The decimal part of the square root of 97 is approximately 0.84885780179. This is closer to 0.5 than 1.
Therefore, 97−−√ is between 9 and 1/2.
To find the whole number and rational number to the nearest half that 97−−√ is between, we can use a number line.
Let's first find the whole number closest to 97−−√.
Since 97 is closer to 100 than to 90, the whole number closest to 97−−√ is 10.
Now let's find the rational number to the nearest half.
To do this, we can see that 97−−√ is closer to 9 than to 10. Therefore, the whole number part of the rational number would be 9.
Next, we need to determine whether 97−−√ is closer to 9.5 or 10.5 on the number line.
To find out, we can calculate the average between 9 and 10:
(9 + 10) / 2 = 9.5
Since 97−−√ is closer to 10.5, the rational number to the nearest half is 10.5.
Therefore, 97−−√ is between 9 and 10.5 on the number line.
When approximating a square root to the nearest half on a number line, we want to find the whole number and rational number that the square root is between.
To find the whole number, we can round down the square root.
The square root of 97 is approximately 9.85. When rounded down, the whole number closest to 9.85 is 9.
To find the rational number to the nearest half, we can determine if the decimal part of the square root is closer to 0.5 or 1.
The decimal part of the square root of 97 is approximately 0.85. This is closer to 1 than 0.5.
Therefore, 97−−√ is between 9 and 1/2.