Uncertainty - Multiplication and Division

TL;DR

Learn how to perform multiplication and division with numbers that have associated uncertainties.

Transcript

in today's lesson we're going to talk about uncertainty mathematical operations associated with uncertainty specifically multiplication and division so let's begin with our first example let's say we have 15.8 plus or minus 0.5 centimeters and we have another number 24.7 plus or minus 0.4 centimeters so what we're going to do in this example is we'... Read More

Key Insights

• 🪜 Uncertainty in multiplication or division can be calculated by finding the percent uncertainty of each number and adding them together.
• 🪜 Adding the uncertainties is necessary, while multiplying them would compound the error.
• 🚱 To convert the percent uncertainty back into a non-percentage value, multiply it by the measured value.
• 📏 The rounded measured values and uncertainties should follow the rules of significant figures.

Questions & Answers

Q: What is the first step in performing multiplication or division with numbers that have uncertainties?

The first step is to calculate the percent uncertainty for each number by dividing the estimated uncertainty by the measured value and multiplying by 100.

Q: Should the uncertainties be multiplied or added when performing multiplication or division?

The uncertainties should be added together when performing multiplication or division.

Q: Why is it important to convert the percent uncertainty back into a non-percentage value?

Converting the percent uncertainty back to a non-percentage value allows for the calculation of the uncertainty in the final result.

Q: How should the measured values and uncertainties be rounded in the final answer?

The measured values should be rounded to the appropriate number of significant figures, considering the original significant figures of the numbers. The uncertainties should also be rounded to the appropriate number of significant figures.

Summary & Key Takeaways

• The video explains how to multiply two numbers with uncertainties by finding the percent uncertainty and adding them together.

• It also demonstrates how to divide two numbers with uncertainties by converting the uncertainties into percent uncertainty and adding them.

• The answers are rounded to the appropriate number of significant figures, considering both the measured values and uncertainty.