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Precision and Significant Figures Notes Precision ______________________________ is how close a series of measurements are to one another; repeatability of a measurement. example: Water is known to boil at 100C. A student boils water 4 times and gets the following data: Trial 1: 65C Trial 2: 65C Trial 3: 67C Trial 4: 66C o Is the student accurate? _____ Why? ________________________________________________ o Is the student precise? ______ Why? ________________________________________________ o __________________ has NOTHING to do with the accepted value! example: Water is known to boil at 100C. A student boils water 4 times and gets the following data: Trial 1: 99C Trial 2: 99.5C Trial 3: 99C Trial 4: 100C o Is the student accurate? _____ Why? ________________________________________________ o Is the student precise? ______ Why? ________________________________________________ • Can measurements be precise but NOT accurate? ____ • Can measurements be precise AND accurate? _____ • Can measurements be NEITHER precise NOR accurate? ____ To Summarize: Accuracy = __________________ (_____________________) Precision = ___________________ (_____________________) Significant Figures Which reading is more precise? 8.50g or 8.503g __________ Why? ____________________________ These numbers are called ______________________________ (sig. figs.). Significant figures represent ____________________________________. Significant figures include all known numbers plus __________________________ number. example: In the number 8.503, the digits known for sure are 8, 5, and 0, but “___” is estimated. Rules for Counting Significant Figures 1. All _________________________________________ ARE significant. examples: 72.3 = ____________ 699.52 = ___________ 2. _____________________________ zeroes are NEVER significant. examples: 0.0025 = ____________ 0.37 = ____________ *Also, these beginning zeroes are NOT sandwiched so they are NOT significant! 3. Zeros ________________________ non-zero numbers are ALWAYS significant – the sandwich rule! examples: 2507 = ____________ 60.5 = ____________ *These zeroes are all “sandwiched” between other sig. figs.! 4. Zeros at the END of a number are significant IF the number has a _______________ point shown. examples: 100.0 = ____________ (decimal shown) 0.1020 = ____________ (decimal shown) 100 = ____________ (no decimal shown – the decimal is implied) 5. Zeros at the END of a number are ___________ significant IF the number has NO decimal point. examples: 0.000 470 = ____________ (decimal shown) 470 = ___________ (no decimal shown – the decimal is implied) LET’S SUMMARIZE THESE SIG FIG RULES! _________________ zeroes = ______________ significant _________________ zeroes = ______________ significant _________________ zeroes = significant ______________ Let’s Practice! Directions: Write the number of significant figures AND identify the appropriate rule. 1. 327 000 m ______ sig. figs. rule: _____ 6. 0.000 02 cm ______ sig. figs. rule: _____ 2. 327 000. g ______ sig. figs. rule: _____ 7. 0.056 00 in ______ sig. figs. rule: _____ 3. 19.0550 kg ______ sig. figs. rule: _____ 8. 1.20 x 104 g ______ sig. figs. rule: _____ 4. 567 mL ______ sig. figs. rule: _____ 9. 5.000 x 102 km ______ sig. figs. rule: _____ 5. 1 800 569 V ______ sig. figs. rule: _____ Do SF show accuracy or precision? ___________ Rounding With Significant Figures st 1 : Underline the number of sig. figs. needed. 2nd: Draw an arrow to the very next number. If the number with the arrow is _____________________, round the last number underlined _____ example: 91.6 rounded to two sig. figs. is _____________ example: 0.0036 to one sig. fig. is _____________ If the number with the arrow is _____________________, leave the last number underlined alone. example: 745.14 rounded to four sig. figs. is ___________ Check to make sure your rounded answer is in the same ballpark as the original number. example: 923 rounded to two sig. figs. is ____________ example: 8 766 rounded to one sig. fig. is ___________ Calculations with Significant Figures ADDING AND SUBTRACTING The final answer must have the ______________________ as the ______________________ measurement. 17.12 cm + 200.4 cm + 74.5 cm + 14.555 cm = 13.00 kg - 0.54 kg - 5.366 kg = MULTIPLYING THE DIVIDING The final answer must have the same number of _____________________ as the ________________________ measurement. Example: 13.91 g / 23.3 mL = _________________ = _________________ calculator answer final sig fig answer Let’s Practice! Directions: Round the following numbers and perform the calculations using the correct number of sig. figs. 1) 56.7 to two sig. figs. _____________ 2) 87 547 to one sig. fig. _____________ 3) 0.000245 to two sig. figs. _____________ 4) 87 547 to two sig. figs. _____________ 5) 2 240 to one sig. fig. _____________ 6) 87 547 to three sig. figs. _____________ 7) 29 920 to two sig. figs. _____________ 8) 25 m x 2 m = _____________ = ______________ calculator answer final sig. fig. answer 9) 25 x 2.0 = _____________ = ______________ calculator answer final sig. fig. answer