Using a number line, what whole number and rational number to the nearest half is 40−−√
between?
explain how 6 and 6.5 is the correct answer
To determine the locations on the number line where 40−−√ is between two numbers, we can start by finding the whole number and rational number (numbers that can be expressed as a fraction) that are closest to 40−−√.
The whole numbers closest to 40−−√ are 6 and 7. However, we are looking for the nearest half, so we need to consider fractions as well.
To find the rational number closest to 40−−√, we can express it as a decimal. Calculating √40, we find that it is approximately 6.3245.
The nearest half to 6.3245 is 6.5.
Therefore, 40−−√ is between 6 and 6.5 on the number line.
To find the whole number and rational number that are closest to √40, we can plot the number √40 on a number line.
First, let's calculate the approximate value of √40:
√40 ≈ 6.3245553 (rounded to 4 decimal places)
Now, we can represent the number line, starting from the nearest whole number less than √40, which is 6, and moving towards the nearest half.
Whole Number and Halves:
4.5 5 5.5 6 6.5 7
Since √40 is approximately 6.3245553, it is closer to 6.5 than it is to 6. Therefore, 6.5 is the rational number (to the nearest half) that √40 is between.
So, the whole number and rational number to the nearest half that √40 is between are 6 and 6.5, respectively.