Using a number line, what whole number and rational number to the nearest half is 40−−√ between?
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?
To determine which whole number and rational number to the nearest half is located between √40 (square root of 40), we can use the number line.
First, let's find the approximate value of √40. The square root of 40 is approximately 6.32455532034.
Now, let's locate the whole numbers nearest to 6.32455532034 on the number line:
Whole number:
... 4, 5, [6], 7, ...
So, the whole numbers nearest to √40 are 6 and 7.
Next, let's find the rational number to the nearest half between these two whole numbers. We can observe that it is located closer to 6 than to 7.
Rational numbers:
... 5.5, 6.0, [6.5], 7.0, ...
Therefore, the whole number and rational number to the nearest half that √40 is located between are 6 and 6.5.
To find the whole number and rational number to the nearest half that 40−−√ lies between on a number line, we can start by simplifying 40−−√.
The square root of 40 is approximately 6.324555320336759, so 40−−√ is approximately 6.324555320336759.
To find the nearest whole number, which is the integer part of the number, we round down to the nearest whole number, which is 6.
To find the nearest half, we look at the decimal part of the number. In this case, the decimal part is 0.324555320336759. We compare it to the values 0.5 and 0, and determine which one is closest.
0.324555320336759 is less than 0.5, but greater than 0. Therefore, the number is closer to 0 than to 0.5.
Thus, 40−−√ is between the whole number 6 and the rational number 0.