Hassan used the iterative process to locate StartRoot 0.15 EndRoot on the number line.

Question

A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5.

Which best describes Hassan’s estimation?
Hassan is correct because StartRoot 0.15 EndRoot almost-equals 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2.

Answer 1

To determine which statement best describes Hassan's estimation of \(\sqrt{0.15}\), let's first calculate the value.

\(\sqrt{0.15} \approx 0.387\).

Now, we can evaluate the options:

1. Hassan is correct because \(\sqrt{0.15} \approx 0.4\). This is a reasonable approximation, as \(0.387\) is close to \(0.4\).

2. Hassan is correct because the point is on the middle of the number line. This statement is vague and doesn't specifically relate to the value of \(\sqrt{0.15}\).

3. Hassan is incorrect because \(\sqrt{0.15}\) is less than \(0.4\). This statement is true, but it suggests that Hassan's estimation is wrong without context. Since estimating it close to \(0.4\) isn't necessarily wrong, this option is less favorable.

4. Hassan is incorrect because the point should be located between \(0.1\) and \(0.2\). This statement is false, as \(0.387\) falls between \(0.4\) and \(0.5\), significantly higher than \(0.1\) and \(0.2\).

Given these evaluations, the statement that best describes Hassan’s estimation is:

Hassan is correct because \(\sqrt{0.15} \approx 0.4\).