Significant Digits and Measurement

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Significant Digits and Measurement
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When measuring

1. There is no such thing as an exact measurement.
2. A digit is considered significant when it is
   known with some reliabilityIn other words, even
   though the last number is an estimate, it is
   significant!

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So how do we express what is significant when
writing?

1. All nonzero digits are Sig. Figs.
2. All final zeros after the decimal are Sig. Figs.
3. Zeros between 2 Sig. Figs. Are Sig. Figs.
4. Zeros used only to mark the decimal place are NOT
   Sig. Figs.Its all about the zeros!

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1) 2.03 2) 1.0 3) 2.00 4) 0.00860 5) 1.0030 6)
967,000 7) 5.10 8) 0.000065 9) 0.009 10)
0.005 11) 0.005670 12) 0.00872 13) 780 14)
78,000 15) 780.000
16) 0.0224 17) 3.000 18) 3000 19) 0.004300 20)
0.00800 21) 0.00967 22) 0.023 23) 4.530 24)
0.90 25) 500 26) 0.1110 27) 54,000 28) 708 29)
780.00 30) 780.0
31) 0.00471 32) 0.0089 33) 230518 34) 1000.1 35)
0.006007 36) 9.6700 37) 7.0200 38) 70,164 39)
0.090 40) 0.00005 41) 0.0076009 42) 0.000008 43)
0.908 44) 0.4900 45) 670,004
3 2 3 3 5 6 3 2 1 1 4 3 3 5 6
3 2 6 5 4 5 5 5 2 1 5 1 3 4 6
3 4 4 4 3 3 2 4 2 3 4 5 3 5 4
It is assumed blue answers do not have zeros that
arose from mere conversion (grams to kg, meters
to kilometers etc)
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Addition and Subtraction

• The result of this type of mathematical process
  must round to the last column of the least
  accurate measurement.

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Multiplication and Division

• Your answer can never contain more Sig. Figs.
  than your least accurate measurement.
• Do the following problem expressing your answer
  with the proper amount of Sig. Figs.6.2 x 3.17?

• 19.654 becomes 19.7

Or does it?
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Only change to proper sig. Figs. at the end of a
computation.