If the measured value of a quantity is 75 with a relative error of 0.04, what is

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Question: If the measured value of a quantity is 75 with a relative error of 0.04, what is the true value?

Options:

Correct Answer: 78

Solution:

Relative error = Absolute error / True value. Let true value be x. 0.04 = |75 - x| / x. Solving gives x = 78.

If the measured value of a quantity is 75 with a relative error of 0.04, what is the true value?

If the measured value of a quantity is 75 with a relative error of 0.04, what is the true value?

Step 1: Understand that relative error is the absolute error divided by the true value.
Step 2: Let the true value be represented by 'x'.
Step 3: Write the formula for relative error: 0.04 = |75 - x| / x.
Step 4: Multiply both sides of the equation by 'x' to eliminate the fraction: 0.04x = |75 - x|.
Step 5: Recognize that |75 - x| means we have two cases to consider: 75 - x or x - 75.
Step 6: Case 1: If 75 - x = 0.04x, then rearranging gives 75 = 1.04x, so x = 75 / 1.04.
Step 7: Calculate x from Case 1: x = 72.12 (not valid since it's less than 75).
Step 8: Case 2: If x - 75 = 0.04x, then rearranging gives x - 0.04x = 75, so 0.96x = 75.
Step 9: Calculate x from Case 2: x = 75 / 0.96.
Step 10: Perform the division: x = 78.125, which we can round to 78.

Relative Error – The ratio of the absolute error to the true value, often expressed as a decimal or percentage.
Absolute Error – The difference between the measured value and the true value.
Algebraic Manipulation – The process of rearranging equations to solve for unknown variables.