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**Measurements and Their Uncertainty 3.1**

Section 3.1-2 3.1 Significant Figures in Measurements

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**Significant Figures in Measurements**

3.1 Significant Figures in Measurements Significant Figures in Measurements Why must measurements be reported to the correct number of significant figures?

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**Significant Figures in Measurements**

3.1 Significant Figures in Measurements Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures. The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

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**Significant Figures in Measurements**

3.1 Significant Figures in Measurements Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.

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**Rules for Significant Figures**

3.1 Rules for Significant Figures Here are the rules to follow when determining how many significant figures one has: Look for a decimal place. It will determine how you analyze the value. If there is a decimal place, do the following “Atlantic/Pacific” method: Start counting from the left hand side (present or Pacific). Ignore zeros at the beginning (left). Start counting at the 1st non-zero digit (1 – 9). Count all of the remaining digits (including zeros). These are the significant digits.

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**Rules for Significant Figures**

3.1 Rules for Significant Figures Start counting from the right hand side (absent or Atlantic). Ignore zeros at the beginning (right). Start counting at the 1st non-zero digit (1 – 9). Count all of the remaining digits (including zeros). These are the significant digits. If there is NO decimal place, due the following:

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**Significant Figures Practice**

3.1 Significant Figures Practice Q: 1,809,000 has how many significant digits? A: Since there is NO decimal, begin counting from the right (RHS), skipping the zeros in the beginning. So, you skip the 1st three (3) zeros and start counting from the “9”. At this point, you count all of the remaining digits. This means that you have four (4) significant figures.

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**Significant Figures Practice**

3.1 Significant Figures Practice Q: has how many significant digits? A: Since there IS a decimal, begin counting from the left (LHS), skipping the zeros in the beginning. So, you skip the 1st two (2) zeros and start counting from the “5”. At this point, you count all of the remaining digits. This means that you have five (5) significant figures including the “0” between the 7 and the 1 and the “0” at the end.

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**Significant Figures in Measurements**

3.1 Significant Figures in Measurements Three differently calibrated meter sticks are used to measure the length of a board. a) A meter stick calibrated in a 1-m interval. b) A meter stick calibrated in 0.1-m intervals. c) A meter stick calibrated in 0.01-m intervals. Measuring How many significant figures are reported in each measurement?

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**for Conceptual Problem 3.1**

2 4 4

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**Significant Figures in Calculations**

3.1 Significant Figures in Calculations Significant Figures in Calculations How does the precision of a calculated answer compare to the precision of the measurements used to obtain it?

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**Significant Figures in Calculations**

3.1 Significant Figures in Calculations In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. The calculated value must be rounded to make it consistent with the measurements from which it was calculated.

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**Significant Figures in Calculations**

3.1 Significant Figures in Calculations Rounding To round a number, you must first decide how many significant figures your answer should have. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.

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3.1

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3.1

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**87.1 meters (round up the “7”) 4.36 x 108 meters 1.55 x 10-2 meters **

for Sample Problem 3.1 87.1 meters (round up the “7”) 4.36 x 108 meters 1.55 x 10-2 meters 9.01 meters (round up the “9”) 1.78 meters x 10-3 (round up the “8”) 630 meters (round up the “.55”)

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**Significant Figures in Calculations**

3.1 Significant Figures in Calculations Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

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3.2

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3.2

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3.2

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3.2

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3.1 Section Quiz 1. A student reports the volume of a liquid as L. How many significant figures are in this measurement? 2 3 4 5

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That’s All Folks ! ! !

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