Created from Youtube video: https://www.youtube.com/watch?v=_TqSI17EUXUvideo**CASE STUDY: ***You are measuring the length of a metal rod. Your initial measurement is 12.345 plus or minus 0.005 meters. You then cut the rod and measure the new length as 7.123 plus or minus 0.002 meters. You need to find the length of the cut piece.***CASE STUDY: ***A biologist measures the volume of a liquid sample as 3.456 plus or minus 0.006 liters. They then add another sample measured at 2.789 plus or minus 0.004 liters. Determine the total volume.***CASE STUDY: ***You are weighing a sample of soil. The initial mass is 50.23 ± 0.02 grams. After drying, the mass is 45.18 ± 0.02 grams. Calculate the mass of water lost.***CASE STUDY: ***You are measuring the length and width of a rectangular sheet. The length is 20.00 ± 0.05 cm and the width is 10.00 ± 0.02 cm. Calculate the area.***CASE STUDY: ***You are conducting an experiment to determine the density of a new material. You measure the mass as 50.00 grams with an absolute uncertainty of 0.010 grams and the volume as 20.0 cubic centimeters with an absolute uncertainty of 0.02 cubic centimeters.***CASE STUDY: ***You are tasked with determining the density of a solution. You measure the mass as 30.00 grams with an absolute uncertainty of 0.006 grams and the volume as 15.0 cubic centimeters with an absolute uncertainty of 0.03 cubic centimeters.***CASE STUDY: ***In a chemistry experiment, you have a mass measurement of 50.00 grams with an uncertainty of 0.05 percent.***CASE STUDY: ***During a physics experiment, you measure a volume of 30.00 cubic centimeters with an uncertainty of 0.20 percent.*

Concepts covered:measurement uncertainties, significant figures, addition and subtraction, multiplication and division, percent uncertainties

This video explains how to perform mathematical operations with measurements that include uncertainties. It covers the rules for adding, subtracting, multiplying, and dividing measurements while maintaining the accuracy and significance of the uncertainties involved.

Table of Contents1.Calculating with Measurement Uncertainties2.Handling Uncertainties in Measurement Operations3.Converting Uncertainties and Calculating Density4.Converting Percentage Uncertainty to Absolute Measurement

chapter

1

Calculating with Measurement Uncertainties

Concepts covered:uncertainties, significant figures, measurements, calculations, accuracy

This chapter explains how to perform mathematical calculations with measurements that include uncertainties. It emphasizes the importance of maintaining significant figures and accurately reflecting the uncertainties in the final results.

Question 1

Adding uncertainties requires keeping two significant figures.

Question 2

Why do we report uncertainties to one significant figure?

Question 3

What is the uncertainty of 4.45 ± 0.0025 grams rounded?

Question 4

All of the following are correct applications of uncertainties except...

Question 5

Select three correct steps to find the total volume.

chapter

2

Handling Uncertainties in Measurement Operations

Concepts covered:subtracting measurements, adding uncertainties, percent uncertainties, absolute uncertainties, calculating uncertainties

The chapter explains how to handle uncertainties when subtracting measurements, emphasizing that uncertainties should be added even when the measurements themselves are subtracted. It also introduces the concept of percent uncertainties for multiplying and dividing measurements, which need to be calculated rather than measured directly.

Question 6

Multiplying measurements requires adding percent uncertainties.

Question 7

How do we handle uncertainties in multiplication?

Question 8

Why do we add uncertainties when subtracting measurements?

Question 9

All of the following are correct applications of uncertainty except...

Question 10

Select three correct steps out of the following...

chapter

3

Converting Uncertainties and Calculating Density

Concepts covered:absolute uncertainty, percentage uncertainty, density calculation, mass measurement, volume measurement

The chapter explains how to convert absolute uncertainties to percentage uncertainties for mass and volume measurements. It then demonstrates the calculation of density using these measurements and how to handle the uncertainties in the final result.

Question 11

Absolute uncertainty can be directly added to percentage uncertainty.

Question 12

How is percentage uncertainty calculated for mass?

Question 13

What is the percentage uncertainty for volume?

Question 14

All of the following are correct applications of uncertainty except...

Question 15

Select three correct steps to handle uncertainties.

chapter

4

Converting Percentage Uncertainty to Absolute Measurement

Concepts covered:percentage uncertainty, absolute measurement, significant figures, unit label placement, measurement accuracy

The chapter discusses the process of converting a percentage uncertainty into an absolute measurement for lab use. It also addresses the placement of unit labels in measurements, highlighting the debate among professionals on the preferred method.

Question 16

Too many significant figures can affect measurement accuracy.

Question 17

What does the uncertainty value represent in measurements?

Question 18

Why is it important to limit significant figures?

Question 19

All of the following are correct applications except...

Question 20

Select three correct steps out of the following...

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