Unit 1: Matter & Measurement Scientific Notation, Accuracy, Precision & Error

unit Measurement number 42.5 g 1.05 mL 16 cm measurement: quantity with _______ and a _____. 42.5 g 1.05 mL 16 cm number unit

A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer

Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

How many places did you move the decimal? 23 2.10,000,000,000,000,000,000,000. How many places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

Express 0.000 000 0902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

1) What is 28750.9 in scientific notation? Let’s Practice! 1) What is 28750.9 in scientific notation? 2.87509 x 10-5 2.87509 x 10-4 2.87509 x 104 2.87509 x 105

2) Which of the following expressions has NOT been correctly changed to sci. not.? 0.00456 = 4.56  10–3 0.0000254 = 2.54  10–5 8,426,000 = 8.426  106 45,200 = 4.52  103 Scientific notation change both numbers to standard and compare (Do these on board)

3) Express 1.8 x 10-4 in decimal notation. 0.00018 4) Express 4.58 x 106 in decimal notation. 4,580,000

Accuracy and Precision and Error Accurate - measurement is close to the actual or true value of whatever is measured. Precise – (repeatable) measurements are close to one another. * precise if only the last digit varies

Accuracy and Precision The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.

Yes! Yes! Practice Problems Three students measure the volume of an object to be 10.4 mL, 10.5 mL, and 10.7 mL. The actual volume is 10.6 mL. Are the measurements accurate? Are the measurements precise? Yes! Yes!

Calculate the average to find out. 2. Five students weigh a sample of metal. Here are their measurements: 2.39 g, 2.60 g, 2.46 g, 2.25 g, 2.58 g The actual weight of the metal is 2.60 g. Are the measurements accurate? b) Are the measurements precise? No Calculate the average to find out. (2.39 + 2.60 + 2.46 + 2.25 + 2.58) = 5 2.46 g No

3. Which set of measurements of a 2.00-g object is the most precise? 2.00 g, 2.13 g, 1.92 g 2.10 g, 2.00 g, 2.20 g 2.05 g, 2.04 g, 2.05 g 1.50 g, 2.00 g, 2.50 g

experimental value – actual value Determining Error The actual (accepted) value is the correct value based on reliable references. The experimental value is the value measured in the lab. Percent error tells you how accurate your results are. experimental value – actual value actual value X 100 % error =

% Error Example 1: Determine the % error if the measured temperature of a solution is 99.1˚C and the actual temperature is 100.0˚C % error = 99.1˚C – 100.0˚C x 100 100.0˚C = 0.9˚C x 100 100.0˚C = 0.9%

% Error Example 2 A technician experimentally determined the boiling point of octane to be 124.1˚C. The actual boiling point of octane is 125.7˚C. Calculate the percent error. Percent error = 124.1˚C – 125.7˚C x 100 125.7˚C = 1.6˚C x 100 125.7˚C = 1.27%