DETERMINING SIGNIFICANT FIGURES

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DETERMINING SIGNIFICANT FIGURES

• Crunching numbers with accuracy and precision

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BEFORE YOU CAN CRUNCH

• You must know which digits are significant
• Because they are going to control the number of
  digits in a calculated figure

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WHAT IS A SIGNIFICANT FIGURE?

• Significant figures are all the digits in a
  measurement that are known with certainty plus a
  last digit that must be estimated.

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WHICH NUMBERS ARE SIGNIFICANT?

• For the purposes of significant figures there are
  two major categories
• Nonzero digits
• 1,2,3,4,5,6,7,8,9
• Zero digits
• 0

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NONZERO DIGITS

• All nonzero digits are significant
• 3269 cm 4 significant figures
• 257 L 3 significant figures
• 1.234567 mm 7 significant figures

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ZEROES

• Zeroes take three forms
• Leading zeroes
• Trapped zeroes
• Trailing zeroes

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LEADING ZEROES

• Leading zeroes are zeroes that come before the
  nonzero digits in a number. They are place
  holders only and are never considered
  significant.
• 0.123 L 3 significant digits
• 0.000012 m 2 significant digits
• 0.003578 mL 4 significant digits

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TRAPPED ZEROES

• Trapped zeroes are zeroes between two nonzero
  digits. Trapped zeroes are always significant.
• 101 s 3 significant figures
• 20013 m 5 significant figures
• 0.3006 cm 4 significant figures (the
  leading zero is not significant)

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TRAILING ZEROES

• Trailing zeroes are zeroes that follow nonzero
  digits. They are only significant if there is a
  decimal point in the number.
• 0.1200 mm 4 significant figures
• 3000 s 1 significant figure
• 250. mL 3 significant figures
• 50.000 g 5 significant figures

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Exact Numbers

• Numbers that were not obtained using measuring
  devices but by counting.
• They can also arise from definitions.
• They can be assumed to have an infinite number of
  significant figures.

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Examples of Exact Numbers

• 2 in 2?r
• 3 and 4 in ¾ ?r3
• Avogadros number is exactly 6.02 x
  1023
• One inch is exactly 2.54 cm

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Now you try

• How many significant digits in each of the
  following
• 1.034 s
• 0.0067 g
• 12 apples
• 3000 m
• 69 people

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Answers

• 1.034 s - 4 significant figures
• 0.0067 g - 2 significant figures
• 12 apples - exact number
• 3000 m - 1 significant figure
• 69 people - exact number