Question

wyatt hiked for 4.7 hours at a rate of 2.9 miles per hour. he determined that he hiked 13.63 miles. which best explains the reasonableness of wyatts answer?

there are two digits to the left of the decimal in the factors and two digits to the left of the decimal in the product, so wyatts answer is reasonable.
there are two digits to the right of the decimal in the factors and two digits to the right of the decimal in the product, so wyatts answer is reasonable.
wyatts answer is reasonable because \\(4 \times 2\\) is 8, and 8 is close to 13.63.
wyatts answer is reasonable because \\(5 \times 3\\) is 15, and 15 is close to 13.63.

Explanation:

Identify the given values and operation

Using the Decimal Multiplication knowledge point

$$
LATEXBLOCK0
$$

Estimate the product by rounding

Using the Rounding Decimals and Estimation knowledge points

$$
LATEXBLOCK1
$$

Evaluate the reasonableness of the answer

Using the Reasonableness of Products knowledge point

$$
LATEXBLOCK2
$$

Since the actual product \(13.63\) is close to the estimated product of \(15\), the calculated answer is reasonable.

Match with the correct multiple-choice option

Using the Reasonableness of Products knowledge point

• Option 1: Discusses digits to the left of the decimal.
• Option 2: Discusses decimal places, which explains decimal placement but not the reasonableness of the product's value.
• Option 3: Uses incorrect rounding (\(4 \times 2 = 8\)).
• Option 4: Correctly rounds to \(5 \times 3 = 15\) and compares it to \(13.63\).

Answer:

• There are two digits to the left of the decimal in the factors and two digits to the left of the decimal in the product, so Wyatt's answer is reasonable.
• There are two digits to the right of the decimal in the factors and two digits to the right of the decimal in the product, so Wyatt's answer is reasonable.
• Wyatt's answer is reasonable because \(4 \times 2\) is 8, and 8 is close to 13.63.
• Wyatt's answer is reasonable because \(5 \times 3\) is 15, and 15 is close to 13.63. (Correct answer)