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
• SDs 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
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• are NOT measured unless
marked.
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200 cm
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• b. 109,000 m
• c. 1,000,000 mm •
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• d. 200 cm
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b.
c.
d.
1 sd to the m
3 sd to the km
1 sd to the km
3 sd to the cm
(a bar over a zero indicates the last measured zero)
• e. 200 cm
• e. 2 sd to the dm
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.
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Samples
a. 0.0032 m
b. 0.01294 g
c. 0.00000002 L
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SDs 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.
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Samples
a. 20.00 g
b. 0.07080 mm
c. 1.0400 cm
d. 45.00
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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
When converting measurements
• Rule: The converted measurement must
have exactly the same precision as the
original measurement.
• Ex. When converting 6.0 cg to dag is the
conversion .006 dag or .0060 dag?
– 6.0 cg has 2 sd so the conversion must have 2
sd. Which conversion has 2 sd?
– Answer: .0060 dag
How to use SD rules when
multiplying/dividing
• Rule: Your calculation (answer) must have
the same precision as the LEAST precise
original measurement
1. 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)
2. Calculate your answer
3. Round the answer to the lowest # of sd found step 1
– 2.40 cm x 3 cm = (7.2 cm2) = 7 cm2