Question

anna drove at a constant rate of 63 miles per hour for 3.2 hours. she determined she drove 201.6 miles. which best explains the reasonableness of annas answer?

there are three digits to the left of the decimal in the factors and three digits to the left of the decimal in the answer, so annas answer is reasonable.
there is one digit to the right of the decimal in the factors and one digit to the right of the decimal in the answer, so annas answer is reasonable.
annas answer is reasonable because \\(60 \times 3\\) is 180, and 180 is reasonably close to 201.6.
annas answer is reasonable because \\(70 \times 4\\) is 280, and 280 is reasonably close to 201.6.

Explanation:

Identify the given values and target

We are given:

• Constant rate: \(63\) miles per hour
• Time: \(3.2\) hours
• Calculated distance: \(201.6\) miles

We need to find the statement that best explains the reasonableness of Anna's answer using estimation.

Round the factors to estimate

Using the Rounding Decimals and Estimation knowledge points:

$$
LATEXBLOCK0
$$

Calculate the estimated product

Using the Reasonableness of Products knowledge point:

$$ 60 \times 3 = 180 $$

Compare the estimate to the calculated answer

Using the Reasonableness of Products knowledge point:

$$ 180 \approx 201.6 $$

Since \(180\) is reasonably close to \(201.6\), the calculation is reasonable. This matches the third option.

Answer:

• (A) There are three digits to the left of the decimal in the factors and three digits to the left of the decimal in the answer, so Anna's answer is reasonable.
• (B) There is one digit to the right of the decimal in the factors and one digit to the right of the decimal in the answer, so Anna's answer is reasonable.
• (C) Anna's answer is reasonable because \(60 \times 3\) is \(180\), and \(180\) is reasonably close to \(201.6\). (Correct answer)
• (D) Anna's answer is reasonable because \(70 \times 4\) is \(280\), and \(280\) is reasonably close to \(201.6\).