GHS Enriched Chemistry Chapter 2, Section 3 Accuracy versus Precision Accuracy Accuracy is how close a measured value is to the actual (true) value. Precision Precision is how close the measured values are to each other. the degree of exactness of a measurement – depends on the measuring instrument

Accuracy and Precision (reference page

Percentage Error Percentage error shows how close your results are compared to the accepted value. It’s a way of showing how well you completed a lab. Complete practice problems 1 and 2 on page 43

Percentage Error – Practice Problems page 43 1. 2.

Error in Measurement Some error or uncertainty always exists in any measurement. Can be caused by human error or the measuring device When we make a measurement, we record all known digits and estimate one digit.

The measuring device determines how you record your measurements!

Significant Figures Significant figures in a measurement consist of all the digits known with certainty plus one estimated digit. Significant figures are critical when reporting data b/c they give the reader an idea of how precise your data is. We don’t worry about significant figures when using “exact” numbers, because they are known with complete certainty.

Why are significant figures important Why are significant figures important? Complete the following density problem: A cube has a volume of 23.5 cm3 and a mass of 18.2 grams. Calculate the density. The calculated answer is .7744680851 g/cm3 Clearly, we cannot express our answer to the tenth decimal place. So how do we round? That’s where sig figs become important!

(These can all be found on page 45 of your text.) Rules for determining significant figures in a measurement. (These can all be found on page 45 of your text.) All nonzero digits are significant: 1.234 g has 4 significant figures (2) Zeroes between nonzero digits are significant: 1002 kg has 4 significant figures

(These can all be found on page 45 of your text.) Rules for determining significant figures in a measurement. (These can all be found on page 45 of your text.) (3) Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: 0.001 oC has only 1 significant figure (4) Trailing zeroes that are also to the right of a decimal point in a number are significant: 0.0230 mL has 3 significant figures

(5) Zeros at the end of a number but to the left of a decimal point may or may not be significant. 190 miles may be 2 or 3 significant figures, 50,600 calories may be 3, 4, or 5 significant figures. 50,600. contains 5 sig figs because of the decimal point.

We can also use scientific notation to indicate the number of sig figs. - the number of significant figures is indicated by the number of numerical figures in the 'digit' term. For example, depending on whether the number of significant figures is 3, 4, or 5, we would write 50,600 calories as: 5.06 × 104 (3 significant figures) 5.060 × 104 (4 significant figures), or 5.0600 × 104 (5 significant figures).

Significant Figures How many significant figures are in each of the following measurements? a. 28.6 g b. 3440. cm c. 910 m d. 0.046 04 L e. 0.006 700 0 kg f. 3.05 x 104 g g. 60.004 mg

Lets try some more. How many significant figures are there in the following measurements: 45.0 cm ______ 1200.0 km ______ .0045 m ______ 1.020 g ______ 6500. m ______ 4.00 L ______ .0025 km ______ 67.003 g ______

Rounding Numbers Sometimes when we perform calculations using measurements, we end up with an answer that has more numbers than we can have When this occurs, we need to round to the required number of sig figs. There are rules that we must follow when rounding numbers. For example, suppose we have to round the following calculations to 3 sig figs: 3.627 cm = 3.621 cm = 3.6251 cm = 3.625 cm = 3.675 cm = 3.63 cm = 3.62 cm = 3.68 cm =

Rounding When we need to drop digits and round, there are set rules we need to follow:

Significant Figures + Addition or Subtraction with Significant Figures When adding or subtracting decimals, the answer must 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. Example: 23.405 cm 16.17 cm +

Now you try a couple! 103.96 g 190.2 g 86.392 km 10.2153 km _ +

Multiplication or Division with Significant Figures For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Examples: 3.2 cm x 1.20 cm = 120.4 g / 3.2 cm3 = 3.84 cm2 37.625 g/cm3 = 3.8 cm2 = 38 g/cm3

a. 5.44 m + 2.6103 m = b. 2.4 m  15.82 m = Sample Problem Significant Figures Sample Problem Carry out the following calculations. Express each answer to the correct number of significant figures. a. 5.44 m + 2.6103 m = b. 2.4 m  15.82 m =

Let’s try a couple practice problems. 4503 + 34.90 + 550 = ? 1.367 - 1.34 = ? 4.56 x 2.5 = ?

Math using sig figs Practice Problems

Addition/Subtraction 34.702 cm 190.450 m + 12.3 cm - 100.5 m 45.0325 g 5.600 km + 12.34 g - 2.30 km

Multiplication/Division 34.5 m x 1.2 m = 1,200 kg x 2.3 kg = 34.6 m / 4.2 = .3400 g / 8.2

Rounding 43.48 cm (to 3 sig figs) = 12.42 cm (to 3 sig figs) = 9.275 g (to 3 sig figs) = 20.35 g (to 3 sig figs) =

Try these problems: 72.49 in 3 sig. fig. is ___________ 292000 in 2 sig. fig. is ___________ 45.52 in 3 sig. fig. is ___________ 92,528 in 4 sig. fig. is ___________ 120.05 in 4 sig. fig. is ___________ 13,052 in 3 sig. fig. is ___________ 239.5 in 3 sig. fig. is ___________ 2.448 x 104 in 3 sig. fig. is ___________ 28.149 in 3 sig. fig. is ___________ 32000.000 in 3 sig. fig. is ___________ 63500 in 2 sig. fig. is ___________ 89999 in 3 sig. fig. is ___________