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SignificantFigures

Honors Chem section 1.5

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Accuracy vs. Precision

• Accuracy: how close a measured value is to the true value.

• Precision: the degree of reproducibility of a measurement. It depends on how well you make a measurement

These terms are often incorrectly used interchangeably

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Examples

• Your summer job is guessing people’s weights at the traveling carnival

• Imagine you have one person who keeps coming back and you guess their weights as:• 56 kg • 65 kg • 70 kg • 51 kg

• The average of these= 60.5kg• If their actual weight is 60kg, the avg

prediction turns out to be accurate, but not precise

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Examples

• If instead you had made guesses of:– 69kg -69kg -67kg -68kg

• Your guesses would be precise, but not accurate

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Precision

• Precision can also mean how detailed the number is– Two Scales:

• Scale #1 = 180lbs• Scale #2 = 180.49lbs

– Which one is more precise?– What is the difference in the scales?

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Does that matter?

• Mass of Obama

• Would it have been ok to report a time as 35 seconds instead of 35.14s?– Would have been OK, but not USEFUL for

Olympic competition

• Could you have timed him so precisely with an analog watch?

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exactly

• Exact #’s– # of people in the room (counting #)– 12 eggs/dz– 1g = 1000mg

• Inexact #’s– #’s obtained by measurement– Always have a level of uncertainty

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Measuring

• Measured quantities are reported in such a way that only the last digit is uncertain

• The number tells you what it was measured with

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measuring

• Always estimate one digit further than the measurement instrument gives (this is the uncertain digit)

• Uncertainties of equipment are given as +/-

+/- 0.01g +/- 0.1g

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Significant Figures

• The way we report numbers tells us how we measured them…hence Significant Figures

• All digits of a measured quantity, including the uncertain one, are called significant figures

• Not all #’s are significant, however – and we will learn to count how many there are

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Examples – How Many Sig Fig’s are In Each Number?

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The Rules• You’ll never find easier rules for significant figures than

these… trademarked at Tennent:

• 2 Conditions:– If there is a decimal point: Begin counting on

the right, and count numbers until there are no more left, or you have hit all zeroes

– If there is no decimal point: Begin counting on the left, and count numbers until there are no more left, or you have hit all zeroes

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?

• Which of the following is an inexact quantity?– A) the # of people in your math class– B) the mass of a penny– C) the # of grams in a kilogram

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?

• Which of the following is an inexact quantity?– A) the # of people in your math class– B) the mass of a penny– C) the # of grams in a kilogram

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Uncertainty

• Which measurement has more uncertainty? What are the uncertainties?

26.1g 26.10g

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Uncertainty

• Which measurement has more uncertainty? What are the uncertainties?

26.10g 26.100g

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Special Conditions• Scientific Notation

• When numbers are written in Scientific Notation, all of the numbers written are significant

• Counting Numbers

• Counting numbers are considered to have an infinite number of sig figs (you’ll see the importance of this in calculations)

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Calculations with sig figs

• Answers can only be as precise as the least precise measurement

• Addition/Subtraction– The answer must have as many digits past the

decimal point as the number with the fewest digits

• Multiplication/Division– The answer must have the same number of significant

figures as the number with the fewest sig figs

Use scientific notation when rounding is difficult

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+/-

– 43.2g + 51.0g + 48.7g = 142.9g

– 258.3kg + 257.11kg + 253kg = 768.41kg

– 0.0487m + 0.05834m + 0.00483m = 0.11187m

– 5.236cm – 3.14cm = 2.096cm

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X & /

– 24cm x 3.26cm = 78.24

– 120m x 0.10lm = 12

– 1.23m x 2.0m = 2.46

– 60.2g / 20.1ml = 2.995024876

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Sig fig calculations

• The result of adding 1.17 x 10-2 and 8 x 10-3 is, to the correct # of sig figs:– A) 1.9 x 10-2

– B) 1.97 x 10-2

– C) 2.0 x 10-2

– D) 0.02– E) none of the above

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Sig fig calculations

• The result of adding 1.17 x 10-2 and 8 x 10-3 is, to the correct # of sig figs:– A) 1.9 x 10-2

– B) 1.97 x 10-2

– C) 2.0 x 10-2

– D) 0.02– E) none of the above

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Sig fig calculations

• (107.36 – 99.2)(5.4033 x 105) = 4.4090928 x 106

• the above calculation, when expressed to the correct number of sig figs is:– A) 4.4 x 106

– B) 4.40 x 106

– C) 4.41 x 106

– D) 4.4090 x 106

– E) 4.091 x 106

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Sig fig calculations

• (107.36 – 99.2)(5.4033 x 105) = 4.4090928 x 106

• the above calculation, when expressed to the correct number of sig figs is:– A) 4.4 x 106

– B) 4.40 x 106

– C) 4.41 x 106

– D) 4.4090 x 106

– E) 4.091 x 106

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Density & Units

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