Transcript Significant figures (download)

SIGNIFICANT figures
Two types of numbers: exact and inexact.
Exact
numbers are obtained by counting or by
definitions – a dozen of wine, hundred cents in a dollar
All
measured numbers are inexact.
All analog measurements involve a
scale and a pointer

Errors arise from:
–
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Quality of scale
Quality of pointer
Calibration
Ability of reader
ACCURACY and PRECISION
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ACCURACY: how closely a number agrees
with the correct value
PRECISION: how closely individual
measurements agree with one another –
repeatability
–
Can a number have high precision and low
accuracy?
Significant figures are the number of
figures believed to be correct

In reading the number the last digit quoted is a best estimate.
Conventionally, the last figure is estimated to a tenth of the
smallest division
2.3 6
2.0
2.1
2.2
2.3
2.4
2.5
The last figure written is always an
estimate
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In this example we recorded the
measurement to be 2.36
The last figure “6” is our best estimate
It is really saying 2.36 ± .01
2.0
2.1
2.2
2.3
2.4
2.5
Precision of measurement (No. of
Significant figures) depends on scale –
last digit always estimated
Smallest Division = 1
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Estimate to 0.1 – tenth of smallest division
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3 S.F.
99.6
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97
98
99
100
Lower precision scale
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Smallest Division = 10
Estimate to 1 – tenth of smallest division
2 S.F.
96
70
80
90
100
Precision in measurement follows the
scale
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Smallest Division = 100
Estimate to 10 – tenth of smallest division
1 S.F.
90
0
100
Measuring length
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What is value of large
division?
–
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What is value of small
division?
–
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Ans: 1 cm
Ans: 1 mm
To what decimal place
is measurement
estimated?
–
Ans: 0.1 mm (3.48 cm)
Scale dictates precision

What is length in top
figure?
–
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What is length in middle
figure?
–
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Ans: 4.6 cm
Ans: 4.56 cm
What is length in lower
figure?
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Ans: 3.0 cm
Scientific notation simplifies large and
small numbers
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1,000,000 = 1 x 106
0.000 001 = 1 x 10-6
234,000 = 2.34 x 105
0.00234 = 2.34 x 10-3
Multiplying and dividing numbers in
scientific notation
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(A x 10n)x(B x 10m) = (A x B) x 10n + m
(A x 10n)/(B x 10m) = (A/B) x 10n - m
Adding and subtracting
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(A x 10n) + (B x 10n) = (A + B) x 10n
(A x 10n) - (B x 10n) = (A - B) x 10n