Chapter 2 Section 3

Measuring & Calculating No experimentally obtained value is exact Human errors Method errors Instrument errors

Measurements Errors can arise depending on the instrument that is used. It is important to use the right instrument Would you use a balance that is calibrated to 1 g to weigh 0.155 g of a substance? Which graduated cylinder would you use from Figure 2-7 to measure 8.6 mL

Accuracy vs. Precision 2 things to consider when making a measurement What is the difference between accuracy and precision?

Accuracy vs. Precision Accuracy: How exact it is The extent to which a measurement approaches the true value of a quantity Example: You measure 35.8 ML Lab partner measures 37.2 mL True volume = 36.0 mL Your measurement is more accurate than your lab partner’s

Accuracy vs. Precision Precision: How closely several measurements of the same quantity made in the same way agree with each other Measure the mass of a substance four times using the same balance 110 g, 109 g, 111 g, and 110 g.

Accuracy vs. Precision The measurements were close to each other so they are precise Remember that precise measurements are not always accurate measurements Ex: If the balance was not reset to zero the measurements are close to each other (precise) but not but not accurate

Significant Figures Significant Figures: Measurement or calculation that consists of all the digits known with certainty plus one estimated or uncertain digit Ex: 10.7834 g is accurate to 5 places The 6th place 00.0004 is the estimated digit

Significant Figures Using the markings on the thermometer we can estimate the temperature to be 28.4 degree C 28.4 is 3 significant figures The first two digits we know for certain The third digit is an estimate The actual temperature is between 28.2 and 28.6 Report the measurements with the correct number of significant figures Example: Measuring temperature with a thermometer marked in intervals of 1 degree C

Significant Figures Burets vs. Graduated Cylinders

Significant Figures Buret vs. Graduated Cylinder 100 mL graduated cylinders are calibrated to the nearest 1 mL Burets are calibrated to the nearest 0.1 mL Best measurement with a graduated cylinder is 25.0 mL – uncertainty is in the tenths place Best measurement with a buret is 25.00 mL – uncertainty is in the hundredths place

Rule Example Zeroes appearing between nonzero digits are significant 40.7 has 3 significant figures 87009 has 5 significant figures Zeroes appearing in front of nonzero digits are not significant 0.009587 has 4 significant figures 0.0009 has 1 significant figure Zeroes at the end of a number and to the right of a decimal point are significant 85.00 g has 4 significant figures 9.070000000 has 10 significant figures Zeros at the end of a number with no decimal point may or may not be significant. Read the rest of 4 in the book 2000 may contain 1-4 significant figures 2000. Has 4 significant figures

Significant Figures Be careful when calculating with significant figures Ex: Mass of a 32.4 mL sample = 25.42 g If we used this information to determine density D = m/v we would get 0.7845689012 g/mL The volume has 4 significant figures while the mass has 3 and the density has 10 So what do we do?

Operation Rule Example Multiplication and Division The answer can have no more significant figures than there are in the measurement with the smallest amount of significant figures 12.257 X 1. 162 ________ 14.2426340 Answer = 14.24 Addition and Subtraction The answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point 3.95 2.879 + 213.6 ------------------ 220.429 Answer = 220.4

Significant Figures Multiplication and Division The answer should have the same number of significant figures as the measurement with the least amount of significant figures Do NOT round until the end when doing calculations

Significant Figures Addition and Subtraction The answer can have no more digits to the right of the decimal than there are in the measurement with the smallest number of digits to the right of the decimal Remember it is only significant figures to the right of the decimal not total significant figures

Significant Figures Exact value: Value that has no uncertainty Has an unlimited number of significant figures 2 categories of exact values Count Values Conversion Factors

Significant Figures Count Values Value that is determined by counting and not by measuring Example a water molecule has 2 hydrogen atoms and 1 oxygen atom No uncertainty in this value because we count the number of atoms NOT measure them

Significant Figures 2. Conversion Factors 1 m = 1000 mm No uncertainty because a millimeter is determined as exactly one-thousandth of a meter 1 mm = 0.001 m Exact values ALWAYS have more significant figures than any other value in the calculation Never use counted or conversion factors to determine the number of significant figures in your calculated results

Scientific Notation Very large and very small numbers are written in scientific notation 2 parts to each value written in scientific notation 1. Number between 1 and 10 2. A power of 10

Scientific Notation 1st part: 2nd part: Move the decimal to the right or left so only 1 nonzero digit is to the left of it 2nd part: Exponent Determined by counting the number of decimal places the decimal point must be moved.

Scientific Notation If the decimal point is moved to the left the exponent is positive If the decimal point is moved to the right the exponent is negative Eliminates the need to count zeroes

Examples are in the Book page 63 Table 2-6 Examples are in the Book page 63 Rule Addition & Subtraction: All values must have the same exponent before they can be added or subtracted. The result is the sum or difference of the first factors all multiplied by the same exponent of 10. Multiplication: The first factors of the numbers are multiplied and the exponents of 10 are added Division: The first factors of the number are divided, and the exponent of 10 in the denominator is subtracted from the exponent of 10 in the numerator

Scientific Notation Table 2-7 on page 64 Questions to Check for Learning Page 64 Problems 5-10 and 12

Additional Problems 1. Determine the # of significant figures in each of the following quantities 218 kPa 0.025 L 200. m2 1.05 g

Additional Problems 2. Round the following quantities to the # of significant figures indicated in parentheses 1. 32.068 km (3) 155.8 g (3) 0.02274 cm (2) 12000 kPa (3)