Significant Figures Honors Chem section 1.5

These terms are often incorrectly used interchangeably 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

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

Examples If instead you had made guesses of: 69kg -69kg -67kg -68kg Your guesses would be precise, but not accurate

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?

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?

exactly Exact #’s Inexact #’s # of people in the room (counting #) 12 eggs/dz 1g = 1000mg Inexact #’s #’s obtained by measurement Always have a level of uncertainty

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

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

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

Examples – How Many Sig Fig’s are In Each Number? 2.00000 6 2000 1 4 2000. 0.00002 1

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

? 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

? 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

Uncertainty Which measurement has more uncertainty? What are the uncertainties? 26.1g 26.10g

Uncertainty Which measurement has more uncertainty? What are the uncertainties? 26.10g 26.100g

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)

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

+/- 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

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

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

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

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

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

Density & Units

Figure: 01-T06 Title: Table 1.6 Caption: Densities of Some Selected Substances at 25ºC