Question

sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. he calculates that he drove 95.7 miles. he knows the answer should be near 80, because \\(40 \times 2\\) is 80. which best explains sebastians actual solution?

• the actual product is reasonable because it is near 80 but greater than 80. both factors were rounded down, making the estimate lower than the actual product.
• the actual product is unreasonable. it should be near 80 but less than 80 because both factors were rounded down.
• the actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
• the actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.

Explanation:

Calculate the actual product

Using the Decimal Multiplication knowledge point

$$ 2.2 \times 43.5 = 95.7 $$

Analyze the estimation process

Using the Rounding Decimals and Estimation knowledge points

$$
LATEXBLOCK0
$$

Evaluate the reasonableness

Using the Reasonableness of Products knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product. (Correct answer)
• (B) The actual product is unreasonable. It should be near 80 but less than 80 because both factors were rounded down.
• (C) The actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
• (D) The actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.