A drink was spilled on the math problem shown below.

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Ron remembers that the second factor was a decimal. Based on the placement of the decimals in the first factor and the product, which must be true of the second factor?
The decimal could be one-tenth.
The decimal could be two-tenths.
The decimal could be five-tenths.
The decimal could be seven-tenths.

1 answer

To determine which of the provided options could represent the second factor, we would need to consider how decimals affect multiplication.

For a multiplication problem involving decimals, the placement of the decimal points in the factors and the product helps us balance the equation.

Generally, if you have a multiplication equation like: \[ \text{first factor} \times \text{second factor} = \text{product} \] then the value of the second factor will largely depend on how many places the decimal is shifted in each of the other values in the multiplication.

To analyze the provided options logically:

  1. If the first factor has 1 decimal place: any second factor with a decimal would affect the product’s decimal placement.
  2. If the product has, say, 1 decimal place, then the second factor could be 1.0, 0.1 (one-tenth), 0.2 (two-tenths), or other numbers regarding how far the decimal shifts.

Let's examine the provided options:

  • One-tenth (0.1)
  • Two-tenths (0.2)
  • Five-tenths (0.5)
  • Seven-tenths (0.7)

Each of these values is a decimal less than or equal to 1, which indicates that they can possibly be valid multipliers depending on the value of the first factor and what the complete product comes out to be.

Without additional context or numerical specifics from the original problem, we can't determine the exact validity of each option conclusively. Therefore, all the values stated could potentially be the second factor depending on the actual values involved in the multiplication.

Thus, it seems that the most logical conclusion is that ANY of the decimals listed could be valid for the second factor, provided the initial conditions of the problem lead to a correct placement of the final product's decimal.

If we were required to choose, “could be” multiple options such as one-tenth, two-tenths, five-tenths, or seven-tenths would be the answer to choices Ron remembers.