Question

stephanie multiplied two decimal numbers and found the product to be 29.648.

which could be the two decimals stephanie multiplied? check all that apply.

13.6 and 2.18
1.36 and 2.18
1.36 and 21.8
13.6 and 0.218

Explanation:

Analyze the digits of the product

Using the Decimal Multiplication knowledge point

$$ 136 \times 218 = 29648 $$

Count the required decimal places

Using the Decimal Places knowledge point

$$ \text{Total decimal places in product} = 3 $$

$$ \text{Decimal places in Factor 1} + \text{Decimal places in Factor 2} = 3 $$

Estimate the product size

Using the Estimation knowledge point

$$
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$$

Evaluate each option

Using the Decimal Places and Estimation knowledge points

• Option 1: \(13.6\) (1 place) and \(2.18\) (2 places). Total places = 3. Estimate: \(13.6 \times 2.18 \approx 29.648\). (Correct)
• Option 2: \(1.36\) (2 places) and \(2.18\) (2 places). Total places = 4. Product would be \(2.9648\). (Incorrect)
• Option 3: \(1.36\) (2 places) and \(21.8\) (1 place). Total places = 3. Estimate: \(1.36 \times 21.8 \approx 29.648\). (Correct)
• Option 4: \(13.6\) (1 place) and \(0.218\) (3 places). Total places = 4. Product would be \(2.9648\). (Incorrect)

Answer:

• [x] 13.6 and 2.18 (Correct answer)
• [ ] 1.36 and 2.18
• [x] 1.36 and 21.8 (Correct answer)
• [ ] 13.6 and 0.218