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Using a number line, what whole number and rational number to the nearest half is sqrt(40) between? (1 point)

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

To determine the whole number and rational number to the nearest half that is closest to √40, let's calculate √40 and round it to the nearest half.

Using a calculator, we find that √40 ≈ 6.3245.

To round it to the nearest half, we need to look at the decimal part: 0.3245.
Since the decimal part is greater than 0.25 but less than 0.75, we round up to the next whole number.

So, to the nearest whole number, √40 is closer to 7.

To find the number to the nearest half, we know that a whole number is equal to a rational number with a denominator of 1. Therefore, 7 as a whole number is also 7/1 as a rational number.

Thus, √40 is between the whole number 7 and the rational number 7/1.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To determine the whole number and rational number closest to √40 on a number line, we can first calculate the exact value of √40.

√40 = 6.32455532034

The whole number closest to √40 is 6, as it is the highest whole number that is less than √40. To find the rational number closest to √40 to the nearest half, we need to determine the two half-intervals that √40 falls between.

6 is the whole number less than √40, and 7 is the next whole number greater than √40. So, √40 falls between the numbers 6 and 7 on the number line.

We can divide the interval between 6 and 7 into halves:

6.5 is the first half, and
7 is the second half.

The rational number closest to √40 is therefore 6.5, as it is the closest rational number to √40 to the nearest half.

User Icon for Explain Bot Explain Bot answered
1 year ago

To determine the whole number and rational number to the nearest half that is between $\sqrt{40}$, we need to first find the two whole numbers that $\sqrt{40}$ is between.

Since $6^2 = 36$ and $7^2 = 49$, we know that $\sqrt{40}$ is between 6 and 7 on the number line.

Next, we need to find the rational number to the nearest half that is between $\sqrt{40}$, 6, and 7.

To find the rational number to the nearest half, we can round $\sqrt{40}$ to the nearest half. $\sqrt{40} \approx 6.32$, which is closer to 6.

Therefore, the whole number and rational number to the nearest half that $\sqrt{40}$ is between are 6 and 6.5, respectively.