Measurement Notes with Precision and Accuracy Part 2

Significant Figures How “good” is your measurement tool? A B C The measurement you record needs to indicate how “good” your measurement tool is! A 3 cm B 3.3 cm C 3.31 cm The last number recorded in a measurement is estimated (your best guess) A 3 cm B 3.3 cm C 3.31 cm The more divisions on your measurement tool, A B C 3 cm 3.3 cm the more precise your measurement can be 3.31 cm (and the more significant figures it will have). Significant Figures Since all measurements are uncertain, we must only use those numbers that are meaningful. In science, that means we record the digits that we are certain of, plus one more that we have to guess. These digits are all referred to as “significant figures”. 3 cm 1 significant figure: we had to take a guess at that one digit 3.3 cm 2 significant figures: we were certain the object was at least 3 cm, but we guessed at the tenths spot. 3.31 cm 3 significant figures: we were certain the object was at least 3.3 cm, but we guessed at the hundredths spot. Significant Figure “Rules” Important when you did not take the measurement directly, and you need to know how many significant figures are in the measurement Non-zero digits: always meaningful, count them as “significant” 22.4 has 3 sig figs Zeros stuck between non-zeros: count them as “significant” 6.022 x 1023 has 4 sig figs Zeros at the beginning of a number less than 1: NEVER count them as “significant” 0.0042 has 2 sig figs Zeros at the end of a number less than 1: ALWAYS count them as “significant” 0.00420 has 3 sig figs Zeros at the end of a number greater than 1 DO count them as “significant” if you see a decimal point DON’T count them as significant if decimal point is absent 290. has 3 sig figs 290 has 2 sig figs NO Rules!!!!!! Atlantic Pacific Rule or how to quickly determine the number of significant figures P A Decimal Present – shoot arrow left to right stop at first number-count 0.00030 2SF 203.47 5SF Decimal Absent – shoot arrow right to left stop at first number-count 789000 4 3SF 1SF How many significant figures in that measurement? The following numbers have 1 significant figure: The following numbers have 2 significant figures: The following numbers have 3 significant figures: 2 2.0 2.00 0.04 0.040 0.0403 80 80. 80.2 700 7.0 x 102 700. How many significant figures in that measurement? The following numbers have 1 significant figure: The following numbers have 2 significant figures: The following numbers have 3 significant figures: 2 2.0 2.00 0.04 0.040 0.0403 80 80. 80.2 700 7.0 x 102 700. Significant Figures Coloring Please color handout according to correct significant figures. Bring up for stamp Rounding Quick rules for rounding: 1) Find the place value you want (the “rounding digit”) 2) Look at the digit just to the right of it: a) If that digit is less than 5, -do not change the rounding digit -drop all digits to the right of it b) If that digit is greater than or equal to five, -add one to the rounding digit -drop all digits to the right of it Examples: 3.04 rounded to 2 sig figs is 3.0 112.511 rounded to 2 sig figs is 110 0.4203 rounded to 2 sig figs is 0.42 Examples: 4.55 rounded to 2 sig figs is 4.6 0.0865 rounded to 2 sig figs is 0.087 40.523 rounded to 2 sig figs is 40. (note the decimal point!) Rounding a Calculated Answer: Addition & Subtraction An answer is no more precise than the least precise measurement used to get the answer. 1) Determine the decimal place of the last significant figure in each of your measured values. 2) Add or subtract in normal fashion. 3) Round the answer to the least precise decimal place seen in the measured values. The problem Rounding when Adding or Subtracting The unrounded The rounded answer answer 9.1 + 4.77 13.87 13.9 211 - 111 100 100. 22 - 0.934 21.066 21 Why? The last sig fig in 9.1 is in the tent place. The last sig fig in 4.77 is in hundredths place. You must round your answer to h last sig fig in the tenths place. The last sig fig in 211 is in the one place. The last sig fig in 111 is also ones place. You must round your answer to h last sig fig in the ones place. The last sig fig in 22 is in the ones The last sig fig in 0.934 is in the thousandths place. You must round your answer to h Rounding a Calculated Answer: Multiplication & Division An answer is no more precise than the least precise measurement used to get the answer. 1) Determine the total number of significant figures in each of your measured values. 2) Multiply or divide in normal fashion. 3) Round the answer to the fewest total number of significant figures seen in the measured values. Rounding when Multiplying or Dividing The problem 27.81 x 20.5 The unrounded answer 570.105 The rounded answer 570. 710 ÷ 3.0 236.6666667 240 0.02 x 2.371 0.04742 0.05 Why? 27.81 has 4 sig figs 20.5 has 3 sig figs You must round yo answer to have 3 si 710 has 2 sig figs 3.0 has 2 sig figs You must round yo answer to have 2 si 0.02 has 1 sig fig 2.371 has 4 sig figs You must round yo answer to have 1 si