significant figures - pharmaceutical analysis

8/18/2019 Significant Figures - Pharmaceutical Analysis

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Significant Figures


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What is a signif icant f igure?

There are 2 kinds of numbers:

– Exact: the amount of money in your account. Known with

certainty.

– Approximate: weight, height —

anything MEASURED. No

measurement is perfect.

– The number of significant figures in a result is

simply the number of figures that are knownwith some degree of reliability. The number 13.2

is said to have 3 significant figures. The number

13.20 is said to have 4 significant figures


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When to use Signif icant f igures

• When a measurement is recorded only thosedigits that are dependable are written down.

• If you measured the width of a paper with your ruler

you might record 21.7cm.

To a mathematician 21.70, or 21.700 is the same.

21.700cm to a analyst means the measurement is

accurate to within one thousandth of a cm.If you used an ordinary ruler, the smallest marking

is the mm, so your measurement has to berecorded as 21.7cm.


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Rules for significant figures

• Rule : All digits are significant

starting with the first non-zero digiton the left.

• Exception to rule : In whole numbers that

end in zero, the zeros at the end are notsignificant.


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How many sig figs?

• 7

• 40• 0.5

• 0.00003• 7 x 105

• 7,000,000

• 1

• 1• 1

• 1• 1

• 1


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• 2 nd Exception to rule : If zeros are

sandwiched between non-zerodigits, the zeros become significant.

• 3rd Exception to rule : If zeros are

at the end of a number that has a

decimal, the zeros are significant.

• These zeros are showing how accuratethe measurement or calculation are.


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How many sig figs here?

• 1.2

•

2100• 56.76

• 4.00

• 0.0792

• 7,083,000,000

• 2

•

2• 4

• 3

• 3

• 4


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How many sig figs here?

• 3401

•

2100• 2100.0

• 5.00

• 0.00412

• 8,000,050,000

• 4

•

2• 5

• 3

• 3

• 6


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What about calculations with

sig figs?• Rule: When adding or

subtracting measurednumbers, the answer can have

no more places after thedecimal than the LEAST of

the measured numbers.


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Add/Subtract examples• 2.45cm + 1.2cm = 3.65cm,

• Round off to = 3.7cm

•

7.432cm + 2cm = 9.432round to 9cm


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Multipl ication and Division

• Rule: When multiplying

or dividing, the resultcan have no more

significant figures thanthe least reliable

measurement.


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A couple of examples

• 56.78 cm x 2.45cm = 139.111 cm2

• Round to 139cm2

•75.8cm x 9.6cm = ?


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2000 ml 0.2 ml 20.00 ml 20 ml

52.50 g .0900 g .0042 g 1.0000 g

4.0 cm 40 mm 40. mm .0040m


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Summary1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are

ALWAYS significant.

2) ALL zeroes between non-zero numbers are

ALWAYS significant.

3) ALL zeroes which are SIMULTANEOUSLY tothe right of the decimal point AND at the end of

the number are ALWAYS significant.

4) ALL zeroes which are to the left of a writtendecimal point and are in a number >= 10 are

ALWAYS significant.

significant figures - pharmaceutical analysis

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