Significant Figures

1
Significant Figures

• You will need to know this stuff ALL year long.

2
Significant Figure Rules

1. All Whole (nonzero) Numbers are Significant
2. Zeros appearing between nonzero numbers are
   always significant
3. Zeros to the right of a decimal and to the right
   of a nonzero number are significant
4. Zeros that are in front of nonzero digits (place
   holders) are NOT significant figures
5. If a decimal is set in a number assume of sig.
   figs.

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1. All Whole (nonzero) Numbers are Significant

• Ex 2.22 Has 3 sig. figs.
• Ex 2.269 Has 4 sig. figs.
• Ex 2.89 x 103 Has 3 sig. figs.
• Practice
• 3.52
• 2.2
• 1.5 x 107

3 sig. figs.
2 sig. figs.
2 sig. figs.
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2. Zeros appearing between nonzero numbers are
always significant

• Ex. 101 3 sig. fig.
• Ex. 40.01 4 sig. fig.
• Practice
• 56.001
• 20.202

5 sig. figs.
5 sig. figs.
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3. Zeros to the right of a decimal and to the
right of a nonzero number are significant

• Ex. 11.00 4 sig. fig.
• Ex. 101.00100 8 sig. fig.
• Ex. 1.0010 5 sig. fig.

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4. Zeros that are in front of nonzero digits
(place holders) are NOT significant figures

• Ex. 0.000333 3 sig. fig.
• Ex. 0.00000009 1 sig. fig.
• Ex. 0.00101 3 sig. fig. (dont forget
  the first rule All whole s are significant)

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5. If a decimal is set in a number assume of
sig. figs.

• Ex. 100. 3 sig. figs.
• Ex. 100 1 sig. fig.
• Ex. 4050. 4 sig. figs.
• Ex. 4050 3 sig. figs.
• Practice Problems 1-6

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Practice Problems on WS

1. 1.0070 m
2. 17.10 kg
3. 100 890 L
4. 3.29 x 103 s
5. 0.0054 cm
6. 3 200 000 g

5 sig. figs.
4 sig. figs.
5 sig. figs.
3 sig. figs.
2 sig. figs.
2 sig. figs.
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Rounding to a specific of Sig. Figs.

• 382748 to 3 sig. fig. 383000
• 0.00876546 to 2 sig. Fig.
  0.0088
• 101010 to 3 sig. fig. 101000

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Rule for Multiplication and Division

• The answer should be rounded off to the same of
  significant figures as the measurement with the
  fewest significant figures.

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Multiplication and Division

• Ex. 12.34 cm x 4.45 cm
  54.913 cm2 round answer to 54.9 cm2
• Ex. 54909 g/304.4 ml 180.3843627
  g/ml round answer to 180.4 g/ml

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Rule ForAddition and Subtraction

• Answers must be rounded so the answer will
  contain the same of digits to right of decimal
  point as the measurement w/ the smallest of
  digits to right of the decimal point.

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Addition and Subtraction

• Ex. 3.3333 m 7.77 m
  11.1033m round to 11.10 m
• Ex. 0.098765 cm - 0.0072
  cm 0.091565 cm round to 0.0916 cm

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Scientific Notation

• All the rules apply to the number part not the
  exponent part.
• Round the following to 3 sig figs.
• 112 000
• 1.12 x 105 This has 3 sig. fig.

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Scientific Notation

• Scientist often deal with very small and very
  large numbers, which can lead to a lot of
  confusion when counting zeros. We have learned to
  express these numbers as powers of 10.
• Converting Rules
• Look At Measurement
• Decide if the is larger than 10 or smaller than
  10
• If larger, move the decimal to the LEFT.
• If smaller than 10, move the decimal to the
  RIGHT.

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Scientific Notation

• Ex Convert 1,500,000 to scientific notation
• Move the decimal point so that there is only one
  digit to its left. A total of 6 places and the
  exponent is positive.
• 1 500 000 1.5 x 106

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Scientific Notation

• Ex Convert 0.000025 to scientific notation. Move
  the decimal point 5 places to the right. Note
  that when a number starts out less than 1, the
  exponent is always negative.
•  
• 0.000 025 2.5 x 10-5