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Accuracy, Precision, and Significant Figures
Accuracy – The extent to which a measurement approaches the
true value of a quantity
Precision – the extent to which a series of measurements of the
same quantity made in the same way agree with one another
**precision conveys nothing about accuracy
Think of 4 targets
Percent error – used to compare the accuracy of the average
experimental value with the correct or accepted value.
Percent error = Value accepted – Value experimental
x 100%
Value accepted
Example: A handbook give the density of calcium as 1.54 g/mL.
What is the percent error of a density calculation of 1.25 g/mL
based on lab measurements?
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For your information:
Scientific Notation  used to express large or small numbers
General Format: Z.ZZ x 10x
For large numbers the exponent is positive
For small numbers the exponent is negative4
Examples: 602000 becomes 6.02 x 105 (the decimal place was
moved over 5 places)
0.000035 becomes 3.5 x 10-5
**Entering scientific notation on calculator
Enter 6.02 x 105
Press 6 . 0 2 EE or exp 5
NOT
6 . 0 2 x 1 0 ^ 5
**You must use the EE button or EXP button.
Significant Figures
Significant figures – any digit in a measurement that is known with
certainty plus one final digit, which is somewhat uncertain or
estimated.
Measurements – are never exact, always rounded off with the last
digit an estimate
Exact numbers – are no rounded off
Example: how many eggs are in a dozen? People in this
room?
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Determining sig figs
56,000 people attended a Vikings game. What place is it
rounded to?
Estimated digit: 6  2 sig figs (zeros are not
significant)
Ruler:
Draw the ruler
Counting Sig Figs
Ask 2 questions
1. Find the first nonzero digit
2. Is there a decimal point
a. No  find the last nonzero digit
(it’s estimated) 2500  2 s.f.
b. Yes  find the last digit zero or nonzero
3.503  4 s.f.
Rules for determining significant figures
Handout from Ms. D
Practice problems
1.030 cm
0.00320 m
2074000 s
601500 km
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0.00001 g
1570500 cm
0.00080 kg
47000 m
367.52 g
0.1020 l
2500.00 m
0.700 L
Rules for Rounding off numbers
If the digit immediately to the right of the last significant digit you
want to retain is:
1. Greater than or equal to 5
Increased by 1 42.68  42.7
2. Less than 5
Stay the same
17.32  17.3
Practice problems
63.47 (3)
90.45 (3)
102.53 (4)
156.15 (4)
2623 (2)
9.335 (3)
0.0465 (2)
24.850 (3)
Scientific Notation
When determining sig figs in scientific notation, only worry about
the number not the x 10x.
Examples: 2.02 x 103  3 sig figs
3.9565 x 10-16  5 sig figs
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Significant Figures in Calculations
Multiplication and Division: Answer should have the same
number of sig figs as the least specific number in the problem
52.8
(3 s.f.)
x
1.0258
(5 s.f.)
=
54.16624
(3 s.f.)
=
54.2
Addition and Subtraction: Answer is rounded to same place as
least specific number in problem
**HINT: Line numbers up vertically
625.3 + 2.005 =
625.3
+ 2.005
627.305  627.3
1323
+ 2500
3823  3800
Exact Conversion Factors
-No uncertainty and do not limit the number o digits in a
calculations
-They result from definitions or counting
1000 mm = 1 m
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Dimensional Analysis or Factor Label Method
1. Write down what you know
2. Multiply by a conversion factor
a. Put the unit you want to cancel out on bottom
b. Put the unit you want on top (numerator)
3. Do the math
a. If in numerator multiply
b. If in denominator divide
1A = 26 Z  this is a conversion factor
Problem: How many Z’s are in 56 A’s
1A = 26 Z
1Z = 25 B’s
Problem: How many B’s are in 19 A’s
***Remember when determining the number of sig figs
conversion factors are exact numbers
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METRIC CONVERSIONS
Basic Unit
Length
Name
Abbrev.
liter
Mass
s
Prefix
mega
Conversion
Abbrev.
Factor
M
1 Mm =
1,000,000
Power of
10
106
Multiplier
1,000,000
Kilo
BASE UNIT
deci
0.1
10-2
c
micro
nano
m

n
1 mm = 0.001
m
10
-9
0.000001
0.00000000
1
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One Step Metric Conversion
7.84 m  cm
1. write what you know
2. Multiply by a conversion factor
a. Put what needs to be canceled on the bottom
3. Put what you want to go to on top
4. Put a 1 by the abbreviation with 2 letters
5. Put the multiplier from table above
6. Do the math
Two Step Metric Conversions
33.0 mL to cL
1. Convert to the base unit
a. mL to L
2. Convert to final unit
a. L to cL
Bridge Conversions
**** 1 mL = 1 cm3
****
Convert 54.3 mL to cm3
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Squared and Cubed Conversions
*In my experience students who right out m3 (m x m x m) tend to
get the correct answer, because they remember to multiply the
conversion factor 3 times
Convert 1.234 m3 to cm3
Convert 83 m3 to L
Density Conversions
1. Write the problem out the fraction way not the cookbook way
2. Convert the top unit, ignoring the bottom unit
3. Convert the bottom unit ignoring the top unit
4. Do the math
Convert 34.5 g/mL to dg/L
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Density Information
 Density – the ratio of mass to volume
Density = mass / volume
 Units usually are g/mL or g/cm3
 Density of water is 1.00 g/ml
 If something floats density < 1 if something sinks density > 1
Determine density of a 343 g object that occupies 1033 cm3 of
space?
Density is a conversion facto that is not exact and must be
considered when determining the number of sig figs.
How much does a piece of aluminum weigh if it has a density of
2.702 g/cm3 of space?
Conversion factor- do not start with this information
Conversion factor may be written two ways (write in)
Work and answer