Objective: In this lab exercise we will be discussing measurement accuracy and precision, significant figures, and scientific notation. The notion of measurement accuracy and precision is essential to properly communicating results of a measurement and the final uncertainty in a measurement can be no better than the measurement with the lowest level of accuracy. For example, if you know you are traveling, in a car, at exactly 65 miles per hour for exactly 1 hour. Then you know you traveled exactly 65 miles. However, there is actually uncertainty in the measurement. In practice if you claim you are traveling 65 miles per hour as read on a speedometer with 1 mile per hour resolution then convention states you are traveling 65 1 1 mph. Similarly, if your watch has resolution of only 1 second then you know your travel time is 1 hr 1 1 sec which we can rewrite as 1 0.0003 hrs. This would be the most accurate way to express the uncertainty. But we might just choose to write out that we traveled for 1.000 hrs where we chose to round to 4 significant figures. It should be clear in this case the more significant uncertainty in the determination of how far you actually drove in the hour is the speed at which you are traveling. Therefore, one can not claim a distance traveled better than the uncertainty in the speed. That is to say when you multiply (65 mph x 1.000 hrs = 65 miles) you can't claim you drove 65.000 miles since the uncertainty is dominated by the resolution of the speedometer. In this lab exercise we will first complete a worksheet involving measuring the length of an object using the rulers supplied in this handout. We will then perform an exercise involving accuracy versus precision, followed by a few exercises related to expressing numbers using scientific notation and performing relatively simple calculations concentrating on making sure to express the final answer with the correct significant figures. Finally, you will be running a simulation to determine the spring constant of a spring using several different methods. The formulas to determine the spring constant are given to you in this handout. Your job will be to perform the measurements and also determine which method leads to the most accurate result and why.Materials: This handout, printed . A pencil or pen with length -15 cm (6 inches). Don't worry about being very close to this length, a common pencil or pen is between 14 and 16 cm. Attendance or viewing mini-lecture on significant figures and scientific notation. Computer and Internet access to use the following simulation: https://phet.colorado.edu/sims/html/masses-and-springs-basics/latest/masses-and-springs- basics en.html Investigation A: Resolution of a Ruler Purpose: To understand that the resolution of a measurement device determines how precise of a measurement you can make.Investigation B: Introduction to Significant Figures Purpose: To introduce the concept of significant figures, and the learn rules for determining the number of significant figures in a given quantity. Introduction: Significant figures are also called "sig figs" are the numbers that determine the precision of a measurement. So what do we mean by precision? As the number of tick marks increased with each scale, your measurements and the measurements made by another person, of the same pencil, will have greater agreement. For example, using the Ist scale you and another person may easily differ by 1 or more. Youmight consider testing this by asking a friend to measure the same pencil with the same scale. With the 2nd scale your measurements when compared with someone else's measurement will only dier by a few tenths. If you compare your measurements by the 3rd scale at most the measurements should have differ by only a few hundredths. So, the ner the scale the closer your measurement will be to those measurement's made by another person. Procedure: 1) Precision deals with the \"spread" of measurements among a group of measurements. A set of measurements with veryr little spread has high precision. In the pictures below, each dart represents a measurement you've taken and the bullseye of the dartboard represents the true value of the quantity you are trying to measure. Rate the set of measurements below in order from most precise, to least. Explain your reasoning. 2) Accuracy deals directly with how close a measurement is to an accepted value. Precision does not determine the accuracy of a measurement. Proper calibration is needed for that. So even though you may have very little spread in your measurements, you do not know whether your measurements are close to the true value unless your measuring tool is calibrated correctly. In fact the average of many low precision measurements may lead to a higher accuracy than the average of many higher precision measurements. Rate the set of measurements above in order from most accurate, to least. Explain your reasoning.Reported measurements must always be rounded to the proper number of significant figures. The number of significant figures reported tells you something about how precise the measurement was. As a first step, we'll learn how to look at a number (in a lab report or in a data table, for instance) and determine the number of significant figures. The rules for counting the number of significant figures in quantity are as follows: I. All exact numbers have an infinite number of significant figures. For example, if you count that there are 35 people in the room, then treat the number 35 as a quantity known to infinite number of significant figures. II. If there is a decimal point in the number, don't count the leading zeros, but count all other digits as significant. For example: 0.00120 has three significant figures. The reason for this is that the leading zeros in a number with a decimal point don't tell you anything about the precision of the measurement, just the overall size. III. If there is no decimal point, don't count trailing zeros, but count all other digits as significant. For example: 12300 has three significant figures. The reason for this is that the trailing zeros in a number without a decimal point don't tell you anything about the precision of the measurement, just the overall size