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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 100C. A student boils water 4 times and gets the following data:
Trial 1: 65C
Trial 2: 65C
Trial 3: 67C
Trial 4: 66C
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 100C. A student boils water 4 times and gets the following data:
Trial 1: 99C
Trial 2: 99.5C
Trial 3: 99C
Trial 4: 100C
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