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hiro says that a constant of proportionality must be a whole number and cannot be a fraction or decimal.Explain why hiro is incorrect?

User Jacoor
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Final answer:

Hiro is incorrect because a constant of proportionality can be a fraction or a decimal, as seen in examples of earning per task jobs or scale conversions on maps that use such non-whole numbers as constants.

Step-by-step explanation:

Hiro is incorrect in saying that a constant of proportionality must be a whole number and cannot be a fraction or decimal. In mathematics, a constant of proportionality is the factor that relates two variables that are directly proportional to each other. It is the value that can multiply the input to get the output in a proportional relationship.

For example, if we consider the formula for calculating pay in a job where you earn a fixed amount per task, say p = 2.50n, where p is your pay and n is the number of tasks you complete. Here, the constant of proportionality is 2.50, which is not a whole number but a decimal. This example demonstrates that the constant of proportionality can indeed be a fraction or a decimal.

Moreover, when we deal with scaling objects or convert measurements, the scales or conversion factors often involve fractions or decimals. For instance, a unit scale on a map could be 1 inch equals 100 feet; when written as a ratio, this is 0.5/100, which shows a decimal constant of proportionality.

User James Elliott
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