Measurements
Measurements Measurements are quantitative observations. What are some kinds of quantitative observations you might make? Temperature Volume Length Mass
Student A and Student B measured the same paperclip. Student A recorded a measurement of 1.0 inches. Student B recorded a measurement of 2.54 cm. What happened?
Units Units tell us what scale or standard of measurement is being used. A unit of measurement is a defined quantity. In science, the SI system (international system) is used. Length Mass Volume Time Temperature meter (m) kilogram (kg) liter (L) seconds (s) kelvin (K)
Prefixes Prefixes change the size of the units and are added before (pre) the base unit. The metric system prefixes are base 10 > Each "step" is either: 10 times larger 10 times smaller King Henry Died (by) Drinking Chocolate Milk
Uncertainty in Measurements When we make measurements, there is always a level of uncertainty. They come from two sources: > Equipment limitation To how many decimal spaces can a ruler measure the length of something? Which equipment is better for measuring the volume of liquids: a beaker or a graduated cylinder? > Human error People might perceive measurements slightly differently or not use equipment consistently.
Accuracy and Precision We need to evaluate our data for uncertainty. Go back to your exploration: what definitions of accuracy and precision did you come up with? Precision How closely grouped a series of measurements are to each other. Accuracy How close to the actual or accepted value a series of measurements are.
Accuracy Accuracy can be measured by percent error:
Example 1: Calculate the percent error for the following: A student determines the density of an unknown metal to be 1.54 g/cm 3. The accepted value of the density of the metal is 1.61 g/cm 3.
Example 2: Which of the following students' data is most accurate? Most precise? The actual density is 1.59 g/cm 3.
Significant Figures When we record measurements, we have to make sure that we only record as many digits as we can actually measure. > That is, we have to express our uncertainty in our measurement. Significant figures or sig. figs. are the recorded numbers of a measurement. It includes > All of the certain digits > and one uncertain digit
Significant Figures: What does that look like? Lets look at an example... 1 2 3 4 5 6 7 8 9
Example 3: Read the volume using the correct significant figures.
How can we minimize uncertainty and error in our measurements? *Brainstorm 3 ideas with your elbow buddy. What are 3 important things to remember when making measurements? *Brainstorm with your elbow buddy.
Determining the number of sig figs Ignore leading zeros Ignore trailing zeros, unless they come WITH a decimal point. Everything else is significant. Exact numbers (conversions, counting numbers) have infinite # of sig figs. Example: > 0.0005811000 > 23000 Exceptions: Exact numbers (counted numbers) and definitions have unlimited sig figs!
Determining the number of sig figs Pacific-Atlantic Present Absent Stop at the first nonzero digit, then count all the digits.
Example 4 Determine the number of sig figs in the following measurements: 9870 m 0.00113 cm 657.13 g 100.00 lb 71,005 km
Operations with significant figures is not required but good to know for future science classes!
Operations with Sig. Figs. When measurements are used in calculations, the result needs to maintain the degree of uncertainty from the measurements. There are two sets of rules: > multiplication and division > addition and subtraction
Multiplication and Division When multiplying or dividing measurements, the final answer can only have as many significant figures as the measurement with the fewest. For example: 2.30 cm x 1.5 cm x 19.02 cm = 65.619 cm 3 "calculator answer" 2.30 cm x 1.5 cm x 19.02 cm = 66 cm 3 Correct answer with sig figs.
Addition and Subtraction When adding or subtracting measurements, the answer can only have as many decimal places as the measurement with the smallest number of decimal places. For example: 23.5 cm + 2.544 cm + 31.03 cm = 57.074 cm 23.5 cm + 2.544 cm + 31.03 cm = 57.1 cm "calculator answer" Correct answer with sig figs.
Example 5 Complete the following using sig figs: 4.55 + 3.0 = 5.1/1.33 = (5.67 x 12)/.098 = 991.0 x 65 = 890.11-433.0198 = 354 + 312 + 481.3 =