Corresponds to “Chapter 3” & “Appendix C: Math Handbook” (pgs R56-63)

 Measurement  A quantity that has both a NUMBER and a UNIT ▪ Units are metric*  Scientific Notation  Product of a coefficient and 10 raised to a power ▪ Coefficient must be 1 ≤ # ≥ 9 ▪ 10 0 = 1 ▪ 10 1 = 10 ▪ Use “EE” or “EXP” or “E” button ▪ means “times 10 to the”

 Accuracy  Measure of how close a measurement comes to the actual or true vale of whatever is measured ▪ How close to the bulls-eye did your dart(s) land?  Precision  Measure of how close a series of measurements are to one another ▪ How close together are all your darts? (regardless of proximity to bulls-eye)

EError = experimental value – accepted value EExp value = measured in lab AAccepted value = correct value based on reliable references or formulas %% error = l error l x 100 % accepted ▪%▪% error = (the absolute value of exp – accepted) divided by the accepted value, times 100 to make it a %

 ALL “known” digits + 1 “estimated” digit  Known are digits clearly marked by instrument increments  Estimated is the smallest increment divided by 10 ▪ So if ruler marks off millimeters (0.001 m) then the unknown digit will be the ten-thousandths’ place ( m)… or 0.1 mm  Sig figs can be annoying, but it is important to only record measurements to the most or least precise it can be… ▪ Think adding exactly 1.00mL from an eye-dropper to a gallon of fluid… why bother taking the time to be perfect with the 1.00mL?

 All nonzero digits are significant  1998 m = 4 sig figs  Embedded zeros are significant  2002 L = 4 sig figs  Leading zeros are NOT significant  0.08 g = 1 sig fig ▪ (because could be written as 8 X g…clearly 1 sig fig)  Trailing zeros are NOT sig, UNLESS a decimal point is involved  2010 mg = 3 sig figs, BUT cg = 4 sig figs;  mg = 4 sig figs ▪ although that format is frowned upon because it could and should be written as x 10 3 mg (obviously 4 sig figs still)

 Counted numbers  24 students in the classroom  5 “digits” on my hand  Defined quantities  60 minutes = 1 hour  100 pennies = 1 dollar  100 cm = 1 m

IIf digit ≤4, truncate (drop) 22.22 cm  2.2 cm IIf digit > 5, round up 11.68 cm  1.7 cm IIf digit = 5, look at numbers after OR before IIf there is a NONZERO digit AFTER a 5, round the 5 up (ex: cm  1.3 cm) IIf there is a ZERO or NO DIGIT after a 5, look at the digit BEFORE ▪I▪If digit is EVEN, truncate 5 (ex: cm  1.2 cm) ▪I▪If digit is ODD, round up (ex: 1.15 cm  1.2 cm)

 A calculated answer can NEVER be more precise than the least precise measurement from which it is calculated  Think eye-dropper into gallon again  Think “a chain is only as strong as its weakest link”  Addition & Subtraction  Keep the LEAST number of DECIMAL PLACES ▪ 1.8 mL + 2 mL = 3.8 mL  4 mL (must round to “ones”)  Multiplication & Division  Keep the LEAST number of SIGNIFICANT FIGURES ▪ 1.8 m X 2.71 m = m 2  4.9 m 2 (must round to 2 figures) ▪ Yes, PEMDAS is still in effect

 Based on powers of 10  Common units [with prefixes if needed]  Meter (length)  Gram (mass)  Second (time)  Liter (volume) ▪ If measuring a large item, use a larger unit ▪ If measuring tiny item, use a smaller unit

kilo- khecto hdeka dam, L, g Basic Unit deci dcenti cmilli m

Used to convert the same quantity of something to a new unit Ex: 1 mL = 1 cm 3 (or 1 cc)