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Experiment 0 - Experiment 0 Exploring the Instruments and...

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Experiment 0 Exploring the Instruments and ORIGIN 1 Example Question Question: The unrounded value of length, x, is 2,346.67cm. The unrounded uncertainty, x is 23cm. What is the rounded value of x with rounded uncertainty? Answer: Since the most significant (leftmost) digit of x is not a ‗1‘ the first digi t is rounded. Thus, the rounded uncertainty is 20cm. Since the last significant digit of the uncertainty is the tens place then the value of x must be rounded to this place as well. So x 2,350 20 cm. You could also use Taylor‘s stan dard for rounding to the second digit when the most significant digit is ‗2‘. The answer would then be x 2,347 23 cm. Experiment 0 - Exploring the Instruments and ORIGIN Introduction The goal of this laboratory is to become familiar with some of the tools and techniques you will be using throughout the quarter. Many of these tools will be used for the next several labs (e.g. the oscilloscope), and others you will use during every lab (e.g. ORIGIN software). If you pay close attention to the functions of the various devices you will be examining this week, your future experiments may proceed more smoothly. 1 Data Analysis 1.1 Significant Figures / Rounding Proper analysis of data requires that you are familiar with and use significant figures. Here is a brief review of the rules of significant figures. First, let us define significant digits. Non-zero digits are always significant. Zeros are significant if they occur between non-zero digits (e.g. 504) or if they occur to the right of the decimal point as trailing zeros (e.g. 4.50 10 3 ). Leading zeroes as in 0.00045 are not significant, as they function only as placeholders for the two significant digits. Here are two simple rules for rounding the reported uncertainty: 1. Round your error to one (the first) significant figure unless the first digit is ‗1‘. If it is ‗1‘, keep the next digit too. T aylor also argues that this can be done if the first digit is ‗2‘. 2. Round your value so that its last significant digit is in the same position (or place value) as the last significant digit of the uncertainty.
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Experiment 0 Exploring the Instruments and ORIGIN 2 Question 0.1 You are measuring the mass of a paperclip on a digital scale. The measured value fluctuates between 1.01 and 0.90 grams. What value will you record for the mass and its uncertainty? 1.2 Estimating Uncertainty Each time you wish to determine the value of a measurable quantity there will be an associated uncertainty in that measurement. Even the most precise instrument has limitations. If your measured quantity is consistent over time and the smallest increment of measured precision is greater than random fluctuation, then your rough estimate of error will be the smallest single increment of the used scale. For example, if you measure length with a ruler with hashmarks every 1/16 of an inch, then you would decide which hashmark is closest for your measurement and your uncertainty would be 1/16 of an inch.
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