Question

karissa determines the area of her desk by multiplying 45.72 centimeters and 60.95 centimeters. she states that the area is 2786.634 square centimeters. which best describes the reasonableness of karissas solution?

the solution is unreasonable because \\(50 \times 60\\) is 3,000, not 2,786.
the solution is reasonable because \\(50 \times 60\\) is 3,000, which is close to the computed area.
the solution is unreasonable because there are four decimal places in the factors and only three decimal places in the product.
the solution is reasonable because there are four numbers to the left of the decimal in the factors and four numbers to the left of the decimal in the product.

Explanation:

Identify the given values and operation

Using the Decimal Multiplication and Area of a Rectangle knowledge points

$$
LATEXBLOCK0
$$

Round the factors to estimate the product

Using the Rounding Decimals and Estimation knowledge points

$$
LATEXBLOCK1
$$

Evaluate the reasonableness of the computed area

Using the Estimation knowledge point

$$
LATEXBLOCK2
$$

Analyze the multiple-choice options

We compare our estimation results to the given options:

• Option 1 states the solution is unreasonable because \(50 \times 60 = 3000\). This is incorrect because \(2786.634\) is close to \(3000\), making it reasonable.
• Option 2 states the solution is reasonable because \(50 \times 60 = 3000\), which is close to the computed area. This matches our analysis.
• Option 3 focuses on decimal places, but \(45.72 \times 60.95 = 2786.6340\), where the trailing zero is dropped, leaving three decimal places. Thus, it is not unreasonable.
• Option 4 uses an incorrect rule about digits to the left of the decimal.

Answer:

• The solution is unreasonable because \(50 \times 60\) is 3,000, not 2,786.
• The solution is reasonable because \(50 \times 60\) is 3,000, which is close to the computed area. (Correct answer)
• The solution is unreasonable because there are four decimal places in the factors and only three decimal places in the product.
• The solution is reasonable because there are four numbers to the left of the decimal in the factors and four numbers to the left of the decimal in the product.