Every measurement must have a unit.

Three targets with three arrows each to shoot. Can you hit the bull's-eye? Both accurate and precise Precise but not accurate Neither accurate nor precise How do they compare? Can you define accuracy and precision?

precise and accurate precise but not accurate Precision and accuracy in the laboratory.

systematic error random error Precision and accuracy in the laboratory.

IMPORTANT REMINDER: Your calculator does not know how to do significant figures. YOU must report numbers using the correct number of significant figures. If you trust the number your calculator gives you, you might get the answer wrong!!!! TI or Casio don’t care what grade you get on the test.

Significant Figures  When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.  There are 2 different types of numbers ◦ Exact ◦ Measured  Exact numbers are infinitely important.  Measured number = they are measured with a measuring device so these numbers have ERROR.  When you use your calculator your answer can only be as accurate as your worst measurement.

Exact Numbers An exact number is obtained when you count objects or use a defined relationship. Counting objects are always exact. 2 soccer balls 4 pizzas Exact relationships, predefined values, not measured. 1 foot = 12 inches 1 meter = 100 cm For instance is 1 foot = inches? No, 1 ft is EXACTLY 12 inches.

Measurement and Significant Figures  Every experimental measurement has a degree of uncertainty.  The volume, V, at right is certain in the 10’s place, 10mL<V<20mL.  The 1’s digit is also certain, 17mL<V<18mL.  A best guess is needed for the tenths place.

What is the Length?  We can see the markings between cm.  We can’t see the markings between the  We must guess between.6 &.7.  We record 1.67 cm as our measurement.  The last digit an 7 was our guess...stop there.

Note the 4 rules When reading a measured value, all nonzero digits should be counted as significant. There is a set of rules for determining if a zero in a measurement is significant or not.  RULE 1. Zeros in the middle of a number are like any other digit; they are always significant. Thus, g has five significant figures.  RULE 2. Zeros at the beginning of a number are not significant; they act only to locate the decimal point. Thus, cm has three significant figures, and mL has four.

 RULE 3. Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant m has six significant figures. If the value were known to only four significant figures, we would write m.  RULE 4. Zeros at the end of a number and before an implied decimal point may or may not be significant. We cannot tell whether they are part of the measurement or whether they act only to locate the unwritten but implied decimal point.

Scientific Notation  Scientific notation is a convenient way to write a very small or a very large number.  Numbers are written as a product of a number between 1 and 10, times the number 10 raised to power.  215 is written in scientific notation as: 215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 10 2

To change standard form to scientific notation…  Place the decimal point so that there is one non-zero digit to the left of the decimal point.  Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.  If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Examples  Given: 289,800,000  Use: (moved 8 places)  Answer: x 10 8  Given:  Use: 5.67 (moved 4 places)  Answer: 5.67 x 10 -4

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

How many minutes are in 2.5 hours ? Conversion factor 2.5 hr x 60 min = 150 min 1 hr 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

Wait a minute! What is wrong with the following setup? 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min 24 hr 1 hr 1 min

English and Metric Conversions  If you know ONE conversion for each type of measurement, you can convert anything!  You must memorize and use these conversions: ◦ Mass: 454 grams = 1 pound ◦ Length: 2.54 cm = 1 inch ◦ Volume: L = 1 quart

Why is this stuff important?