Transcript Significant Digits

Significant (Measured) Digits
Measuring with Precision
Significant Digits (sd)
 Defn: Those numbers that result from directly
measuring an object. It shows the precision of the
measurement.
 Units must be included (no units no sd)
 The precision of the measurement depends upon the
measuring instrument
 Use the following PRIORITIZED list to determine the
number of sd’s in a measurement, calculation, or
conversion
Rule 1: All nonzero digits are
significant (they were measured)
 Samples
 a. 234 m
 b. 1678 cm
 c. 0.23 g
 SD’s and precision
 a. 3 sd to the m
 b. 4 sd to the cm
 c. 2 sd to the cg
Rule 2: All zeros between nonzero (or
significant) digits are significant
Translation: In between 0s must be measured
 Samples
 a. 202 mm
 b. 1003 cm
 c. 0.200105 m
 SD’s and precision
 a. 3 sd to the mm
 b. 4 sd to the cm
 c. 6 sd to the mm
Rule 3: Zeros to the right of a nonzero digit but to
the left of an understood decimal are NOT
significant unless otherwise indicated.
Translation: 0s at the end of a whole number
are NOT measured unless
 marked.
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a. 200 cm
b. 109,000 m
c. 1,000,000 mm
d. 200 cm
e. 200 cm
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a.
b.
c.
d.
e.
1 sd to the m
3 sd to the km
1 sd to the km
3 sd to the cm
2 sd to the dm
(a bar over a zero indicates the last measured zero)
Rule 4: All zeros to the right of a decimal point
but to the left of a nonzero digit are NOT
significant.
Translation: 0s in front of a number less than
1 are NOT measured.
 Samples
 a. 0.0032 m
 b. 0.01294 g
 c. 0.00000002 L
 SD’s and precision
 a. 2 sd to the .1 mm
 b. 4 sd to the .01 mg
 c. 1 sd to the .01 mL
Rule 5: All zeros to the right of a decimal point
and following a nonzero digit are significant
Translation: 0s at the end of a decimal
number are measured.
 Samples
 a. 20.00 g
 b. 0.07080 mm
 c. 1.0400 cm
 d. 45.00
 SD’s and precision
 a. 4 sd to the cg
 b. 4 sd to the .01 mm
 c. 5 sd to the mm
 d. 0 sd
How to use this information when
converting/evaluating measures
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Examine the number & go through rules IN ORDER
Rule 1 - underline any nonzero digits
Rule 2 - underline any zeros between these
Rule 3 - place an ‘n’ under the zeros at the end of a
whole number (after any overlined 0s)
 Rule 4 - place an ‘n’ under zeros in front of a number
less than one
 Rule 5 - underline zeros at the end of a decimal
number
 Count the number of underlined digits = # sd
How to use SD rules when
multiplying/dividing
 Rule: Your calculation (answer) must have the same
precision as the LEAST precise original measurement
 Find the number of significant digits in each of the
starting numbers and note the lowest number of
significant digits
 ex. 2.40 cm x 3 cm (lowest # of sd is 1)
 Calculate your answer
 Round the answer to the lowest # of sd found in #1
 2.40 cm x 3 cm = (7.2 cm2) = 7 cm2
Significant Figures
Significant Figures
 All measurements are inaccurate
 Precision of measuring device
 Human error
 Faulty technique
Significant Figures
 Measurements need to convey precision
 Must include degree of uncertainty
 Sig Figs tell us
Significant Figures
Significant Figures
1. Significant figures in a measurement
include
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all of the digits that are known precisely
plus one last digit that is estimated.
Significant Figures
2. Non-zero digits are always significant.
103.230002
Significant Figures
3. All final zeros after the decimal point are
significant.
12.740
0.0420
Significant Figures
4. Zeros between two other significant
digits are always significant.
10.0
2004
6.000
Significant Figures
5. Zeros used only for spacing the decimal
point are not significant.
100
0.00000233
Killing Babies
 Always put a 0 in front of a decimal point

 0.0042 
 .873 
 0.247
Significant Figures
Significant Figures
1) 400
2) 200.0
3)
4)
218
5) 320
6)
0.00530
7)
8) 4755.50
0.0001
22 568
Significant Figures
1) 4.0 x 103
2)
1.67 x 10-8
5 x 1012
4)
2.00 x 104
3)
5) 635.000
6) 22 000
7)
8)
5201
81
Significant Figures
6. If you add or subtract, the answer is
rounded to the same number of decimal
places as the measurement with the least
number of decimal places.
Significant Figures
7. If you multiply or divide two numbers,
the answer is rounded off to the number
of significant figures in the least precise
term used in the calculation (i.e. the
number with the fewest sig figs).
Calculations
Calculations