2 measurements [a andb[are given as 40.10cm and 36.00cm respectively find the percentage error in the quotient a/b

To find the percentage error in the quotient \( \frac{a}{b} \), we need to use the rule for calculating the percentage error in a division operation.

The formula for the percentage error of a quotient is:

\[
\text{Percentage Error of } \left( \frac{a}{b} \right) = \sqrt{\left( \frac{\Delta a}{a} \right)^2 + \left( \frac{\Delta b}{b} \right)^2} \times 100
\]

Where:
- \( a \) and \( b \) are the measured values.
- \( \Delta a \) and \( \Delta b \) are the absolute errors in the measurements.

Since the measurements are given as \( a = 40.10 \, \text{cm} \) and \( b = 36.00 \, \text{cm} \), let's assume that the errors in \( a \) and \( b \) are given by the least count (the smallest decimal place of the measurements), which is \( \Delta a = 0.01 \, \text{cm} \) and \( \Delta b = 0.01 \, \text{cm} \).

Let's calculate the percentage error:

1. Calculate the relative errors \( \frac{\Delta a}{a} \) and \( \frac{\Delta b}{b} \).
2. Apply the percentage error formula.

I'll compute this now.The percentage error in the quotient \( \frac{a}{b} \) is approximately \( 0.0373\% \).

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:
1. How is absolute error different from percentage error?
2. How do we calculate errors for other operations, like multiplication or powers?
3. What are the sources of error in a physical measurement?
4. How do significant figures affect the accuracy of measurements?
5. Can errors in multiple operations be combined?

**Tip:** Always report errors with the same number of decimal places as the original measurement for consistency.

2 measurements [a and b] are given as 40.10 cm and 36.00 cm respectively. Find the percentage error in the quotient a/b.

Learn how to calculate the percentage error in the quotient of two measurements, a = 40.10 cm and b = 36.00 cm, using the error propagation formula for division. This problem demonstrates key concepts in error analysis and is suitable for Grades 11-12.

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