Significant Figures

1
Significant Figures

• (sig figs if youre cool)

2
What are significant figures?

• A process for reporting measurements using the
  number of digits and decimal places that tell you
  how EXACT the measurement is.
• 121 is less exact than 121.5
• The difference a more precise tool was used to
  measure the 121.5
• Reporting 121.5 tells anyone that the person was
  able to measure the quantity up to the tenths
  place.

3
So, why should I care about these?

• When reporting measurements
• You need to know how to report measurements in
  lab correctly (both the measurement and the
  precision of the tool used)
• Calculations with significant figures
• You need to know how to calculate values so you
  dont report answers that are more exact than the
  numbers used to calculate that value.

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Significant Figure Rules

• 1 Non-zero digits are always significant
• 2 Any zeros between two significant digits are
  significant (zero sandwich)
• 3 A final zero or trailing zeros in the decimal
  portion ONLY are significant

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How Many Sig Figs?
Example Number of Sig Figs
23
203
4500
4500.2
0.0012
1.0012
51,003
43,251
8
8.0
2
3
2
5
2
5
5
5
1
2
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Rounding Sig Figs

• Sometimes youll need to round numbers to the
  correct number of sig figs
• For example
• Round 90,970 to 2 sig figs ? 91,000

Example Round to Result
678,510 miles 3
0.0070894 km 4
67,548 kg 2
0.010798 cm 4
679,000 miles
0.007089 km
68,000 kg
0.01080 cm
7
Addition Subtraction

• Significant Figures in Calculations

• Addition Subtraction The number of decimal
  places in the answer should be equal to the
  number of decimal places in the value with the
  fewest decimal places. Round only your FINAL
  answer!

8
Addition Subtraction Problems
175 92.3
82.6 - 2.13
5400 - 234
27,700 - 13
23.457 7
10 5
267.3 round to 267
80.47 round to 80.5
5166
27687
30.457 round to 30
15
9
Multiplication and Division
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Multiplication and Division Problems
82 7
153 / 0.1145
72 2
920.1 / 50.
900 7
54,234.1172 1
574, round to 600
1336.244541 round to 1340
144 round to 100
18.4 round to 18
6300 round to 6000
54234.1172 round to 50,000
Note If your answer is being used in another
equation, use the calculated answer, not the sig
fig answer.
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Scientific Notation

• (all the hip kids are cool with it)

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• To change numbers to scientific notation
• Make sure number is between 1.0 and 9.9
• Count the number of decimal places the decimal
  was moved
• If moved to the left, the exponent is positive
• If moved to the right, the exponent is negative
• On your calculators use EE or EXP to replace
  x10
• Changing numbers to scientific notation will help
  you count numbers of sig figs

54,970,000 5.497 x 107
0.000786 7.86 x 10 -4
23.001 2.3001 x 101
0.0000002456 2.456 x 10 -7