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**UNIT 3 MEASUREMENT AND DATA PROCESSING**

TIER 3 Identify the uncertainties in a particular experiment Construct ways to reduce random errors Apply the rules of significant figures (sig figs) to determine the number of sig figs in a given number State the results of calculations to the appropriate number of significant digits

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**Identify the uncertainties in a particular experiment**

Each instrument has a degree of uncertainty . For example: A digital instrument has a degree of uncertainty of +/- the smallest scale division An analogue instrument such as a graduated cylinder, thermometer etc has a degree of uncertainty of +/- half the smallest division

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**DIGITAL BALANCE 12.58 +/- .01 g THIS BALANCE IS CAPABLE**

OF READING TO THE HUNDREDTH PLACE SO THE MEASUREMENT WOULD BE WRITTEN AS: /- .01 g

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ANALOGUE INSTRUMENTS THIS GRADUATED CYLINDER IS MARKED OFF BY EVERY 2 ml . THEREFORE THE UNCERTAINTY WOULD BE +/- 1ml

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**HOW WOULD YOU EXPRESS THIS MEASUREMENT**

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ANSWER: 38.2 +/- .5 cm3 Each division is 1 cm3 so the uncertainty would be ½ = .5. Always express your data to one estimated digit. Since it is just past the 38 cm3 mark, one person may read it as /- .5 cm3 whereas someone else might read it as /- .5 cm3

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**Construct ways to reduce random errors**

Because random errors have an equal probability of being too high or too low, the best way to reduce this errors is to repeat the measurement as many times as possible. The rule of thumb is to do at least 3 trials if not more. If the same person duplicates the experiment with the same results then it is considered repeatable. If several experimenters duplicate the results then it is considered reproducible.

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SIGNIFICANT FIGURES

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**RULES FOR DETERMINING NUMBER OF SIGNIFICANT DIGITS**

Apply the rules of significant figures (sig figs) to determine the number of sig figs in a given number RULES FOR DETERMINING NUMBER OF SIGNIFICANT DIGITS

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**SIGNIFICANT FIGURES ADDING AND SUBTRACTING**

When adding or subtracting, the answer should be quoted to have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.

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**MULTIPLICATION AND DIVISION**

When multiplying or dividing numbers, the answer should be quoted to have the same number of significant figures that are in the measurement with the fewest number of significant figures

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Rounding off rule #1 If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped. Rounding off rule #2 If the first digit to be dropped is a digit greater than 5, or if it is a 5 followed by digits other than zero, the excess digits are all dropped and the last retained digit is increased in value by one unit. Rounding off rule #3 If the first digit to be dropped is a 5 not followed by any other digit, or if it is a 5 followed only by zeros, an odd0even rule is applied. Odd-Even rule for rounding off: If the last retained digit is even, its value is not changed, and the 5 and any zeros that follow are dropped. If the last digit is odd, its value is increased by one. Intention of the odd-even rule for rounding off: The intention of this odd-even rule is to average the effects of rounding off. ROUNDING RULES

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**How many significant figures do the following numbers have?**

1) 1234 _____ 2) _____ 3) 890 _____ 4) _____ 5) _____ 6) _____ 7) _____ 8) _____ 9) _____ 10) 780. _____ 11) 1000 _____ 12) _____ 13) _____ 14) _____ 15) 8120 _____ 16) 72 _____

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**Solutions to the Significant Figures Practice Worksheet**

1) 4 2) 2 3) 2 4) 4 5) 5 6) 8 7) 3 8) 2 9) 6 10) 3 11) 1 12) 6 13) 1 14) 3 15) 3 16) 2

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**Answers are in RED 583.00 ÷ 83= 7.0 (57.6 X 3) ÷ (34 X 3.00 X 87.507)=**

0.02 = 555 l= 8597 (3.50 X 105) X [2.8 ÷ (5.4 )]= 750000 (6.10 X 107 ) + (3 X 107 )= 9 X 107 787 X 3.0= 2400 Answers are in RED

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THE END

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