Using Scientific Measurements Big idea:  How do we define accuracy and precision.  What are significant figures?  How do we use very large numbers or small numbers?

Using Scientific Measurement Accuracy is different from precision Accuracy - refers to the closeness of measurement to the correct or accepted value of the quantity measured. Precision - refers to the closeness of a set of measurements of the same quantity made in the same way.

Using Scientific Measurements Two technicians independently measure the density of a new substance.  Tech A records the values of 2.000, 1.999, and 2.001 g/ml.  Tech B records values of 2.5, 2.9, and 2.7 g/ml.  The correct value is 2.701 g/ml.  Who was more accurate?  Who was more precise?

Using Scientific Measurement Percentage error - is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100. % error = [Valueexp.- Valueaccpted/Valueaccpted]x100

Using Scientific Measurement A volume is measured experimentally as 4.26 ml.  What is the percentage error, given that the correct value is 4.15 ml?

Using Scientific Measurements Significant figures in a measurement consists of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. Nail example We will follow the rules that are found in your Reference Material.

Significant Figures aka Sig Figs 1. Non-zero digits and zeros between non-zero digits are always significant. 2. Leading zeros are not significant. 3. Zeros to the right of all non-zero digits are only significant if a decimal point is shown. 4. For values written in scientific notation, the digits in the coefficient are significant. 5. In a common logarithm, there are as many digits after the decimal point as there are significant figures in the original number.

Using Scientific Measurements How many significant figures are in each of the following measurements? 28.6 g 3440. cm 910 m 0.046 04 L 0.006 700 0 kg

Using Scientific Measurements Adding or Subtracting with Significant figures When adding or subtracting with 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:  25.1 g - 2.03 g Example:  5400 L - 365 L

Using Scientific Measurements Multiplication and Division with significant figures. For multiplication and division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Example:  3.05 g/8.47 ml Example:  17.982 g/4.13 cm3

Using Scientific Measurements Scientific notation is used to express very large or small numbers. In scientific notation, numbers are written in the form Mx10n, where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number. Example:  6.5x104 km Example:  0.000 12 mm

Using Scientific Measurements Determine M by moving the decimal point in the original number to the left or the right so that only one nonzero digit remains to the left of the decimal point. Determine n by counting the number of places that you moved the decimal point.  If you moved it to the left, n is (+). if you moved it to the right, n is (-).

Using Scientific Measurements Mathematical Operations Using Scientific Notation. Adding and Subtracting 4.2x104 kg + 0.79x104 kg 42x103 kg - 79x103 kg Multiplication 5.23x106 um x 7.1x10-2 um Division 5.44x107 g/8.1x104 mol

Formative Assessment Handout pg. 61 in textbook.  Workout problems 1 through 8.