Significant Digits

1
Significant Digits

• What are they?
• Where do they come from?
• Why do I care?

2
Significant Digits

• The number of significant digits (figures) is a
  measure of the uncertainty of a measurement.
• The greater the number of significant digits, the
  more certain you are of your measurement
• The number of significant digits equals the
  number of digits that are certain, plus one
  additional digit , which is an uncertain digit.

3
Reading a Volumetric Device What is the correct
measurement?
Insert figure 3.13
Note the Meniscus
4
Determine the Number of Significant DigitsNon
Zeros / Sandwiched Zeros

• All non-zero digits are significant
• Zeros sandwiched between two non-zero digits
  are significant

5
Determine the Number of Significant DigitsZeros
with Decimal Point Present

• If the measured quantity HAS a decimal point
• Start at the left of the number and move right
  until you reach the first non-zero digit.
• Count that digit and every digit to its right as
  significant.
• Decimal Present ? Start at the Pacific

6
Determine the Number of Significant DigitsZeros
Without Decimal Point Present

• If the measured quantity DOES NOT HAVE a decimal
  point
• Start at the right of the number and move left
  until you reach the first non-zero digit.
• Count that digit and every digit to its left as
  significant.
• Decimal Absent ? Start at the Atlantic

7
Determine the Number of Significant
DigitsScientific Notation

• Scientific notation can be used to show which
  zeros are significant
• Anything written in Scientific Notation is
  significant

8
How many significant digits does each of the
following numbers have?

• Measurement
• 0.0050 m
• 0.0003056 L
• 9.5 x 103 g
• 56,980. cm3
• 56980 cm3
• 3.7890 x 104 s
• 7000 g
• 120500 mL
• 9.5080 x 103 g

• Sig Figs

9
How many significant digits does each of the
following numbers have?

• Measurement
• 0.0050 m
• 0.0003056 L
• 9.5 x 103 g
• 56,980. cm3
• 56980 cm3
• 3.7890 x 104 s
• 7000 g
• 120500 mL
• 9.5080 x 103 g

• Sig Figs
• 2
• 4
• 2
• 5
• 4
• 5
• 1
• 4
• 5

10
Exact Numbers

• Numbers that are a result of counting are exact
• Definitions contain exact numbers.
• For example 60 s in one min, 1000 mg 1 g, 0.01m
  1 cm
• Exact numbers do not limit the number of
  significant figures in an answer.
• Exact numbers have the number of significant
  digits the calculation requires.

11
Operations with Significant FiguresMultiplying
and Dividing

• When numbers are multiplied and divided, the
  answer has the same number of significant digits
  as measurement with the least number of total
  significant digits.
• 0.00569 x 0.91
• 0.0052
• 9863 ? 876.89
• 11.25

12
Operations with Significant FiguresAddition and
Subtraction

• In addition and subtraction, the answer has the
  same number of decimal places as the measurement
  with the fewest number of decimal places
• 23.560 2.1
• 25.7
• 0.0056 - 0.004067
• 0.0015

13
Rounding

• Answers need to be rounded to the correct number
  of significant figures
• The round a number to the proper number of
  significant figures or decimal points, start at
  the right of the number and remove all digits
  needed to have the correct number of digits.
• If the last digit removed is gt 5, round up.
• If the last digit removed is lt 5 leave the
  remaining last digit the same.