Download Accuracy, Precision, and Significant Figures

Accuracy, Precision, and Significant Figures
Accuracy –
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 ______________________ of the average
experimental value with the correct or ______________________ 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?
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
**You must use the EE button or EXP button.
6 . 0 2 x 1 0 ^ 5
Significant Figures
Significant figures –
Measurements – are never exact, always rounded off with the last digit an estimate
Exact numbers – are not rounded off
Example: how many eggs are in a dozen? People in this room?
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
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
2. Less than 5
Increased by 1
Stay the same
42.68  42.7
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
Significant Figures in Calculations
Multiplication and Division:
52.8
x
1.0258
=
54.16624
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
627.3005  627.3
1323
+ 2500
3823  3800
Exact Conversion Factors
-No _______________ and do not limit the number of digits in a calculation
-They result from definitions or__________________________
1000 mm = 1 m
Dimensional Analysis or Factor Label Method
1.
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_____________________
b. If in denominator ______________________
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
METRIC CONVERSIONS
Basic Unit
Length
Name
Abbrev.
liter
Mass
s
Conversion Factor
Prefix
mega
Kilo
Abbrev.
M
1 Mm = 1,000,000
Power of 10
106
Multiplier
1,000,000
BASE UNIT
deci
0.1
10-2
c
1 mm = 0.001 m
micro
m

nano
n
0.000001
10-9
0.000000001
One Step Metric Conversion
7.84 m  cm
1. write what you know
2. Multiply by a _________________________________________
a. Put what needs to be canceled on the ____________________________
3. Put what you want to go to on top
4. Put a 1 by the abbreviation with 2 ________________________________
5. Put the multiplier from table above
6. Do the math
Example
Two Step Metric Conversions
33.0 mL to cL
1. Convert to the ______________________ unit
a. mL to L
2. Convert to________________________ unit
a. L to cL
Bridge Conversions
**** 1 mL = 1 cm3 ****
Convert 54.3 mL to cm3
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 ________________________ 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
Density Information

Density – the ratio of ____________________ to _____________________
Density = mass / volume

Units usually are g/mL or g/cm3

Density of water is __________________________________

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 factor that is not____________________ 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