You overhear a classmate telling another student that \(1 \mathrm{ft}\) equals \(12 \pm 0.5 \mathrm{in}\). Is this statement correct or incorrect? Why?

Short Answer

Expert verified
The statement is incorrect. The correct conversion factor is \(1 \mathrm{ft} = 12 \mathrm{in}\) without any uncertainty. The given statement introduces an incorrect range of values between 11.5 and 12.5 inches which does not exist in the conversion factor between feet and inches.

Step by step solution

01

Recall the conversion factor between feet and inches

Recall that there are exactly 12 inches in a foot. So, the conversion factor is \(1 \mathrm{ft} = 12 \mathrm{in}\) without any uncertainty.
02

Evaluate the given statement

Now, we can compare this conversion factor with the statement given: \(1 \mathrm{ft}\) equals \(12 \pm 0.5 \mathrm{in}\). The statement implies that 1 foot could be equal to as much as 12.5 inches (\(12 + 0.5\)) or as little as 11.5 inches (\(12 - 0.5\)).
03

Determine if the statement is correct or incorrect

The statement is incorrect, as 1 foot is exactly equal to 12 inches, not a range of values between 11.5 and 12.5 inches. The given statement introduces an uncertainty that does not exist in the conversion factor between feet and inches.

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