Scientific Measurement
Objectives
Convert measurements to scientific notation
Distinguish between accuracy and precision
Define error and percent error
Determine number of significant figures
Describe history of Metric System
List SI measurements and common prefixes
Convert units using dimensional analysis
Solve problems by breaking into steps
1.
Measurement:
quantity that has number and unit.
2) Scientific notation: coefficient X base raised to an
exponent
Rules for Scientific Notation
coefficient = number that is ≥ 1 and <10
base = 10
exponent = number of places decimal is shifted.
4) Accuracy = how close measurement is to true value
5) Precision = repeatability, how close series of measurements are
to each other
7) Accepted value =AV= “true value” , standard value
8)Experimental value = EV =lab measurement
9) Error = EV – AV =experimental value – accepted value
10) Percent error
=
[EV-AV] X 100%
AV
11) Percent error is a number NOT a measurement. [a number
has no units]
12) Remember to use the absolute value of the error
Significant figures
13) Significant figures are numbers that are known with some
degree of reliability
14) The last figure in a measurement is the estimated figure.
15) Rules for sig figs:
a) All nonzero figs ARE significant
b) Zeros between sig figs ARE significant
c) Leading zeros in decimals are NOT significant.
They are space holders
d) Trailing zeros following a decimal
OR followed BY a decimal ARE significant
e) Trailing zeros NOT followed by a decimal are
NOT significant
f) Exact numbers have unlimited sig figs.
g) All numbers in coefficient in scientific notation
ARE significant.
h) moving the decimal point does NOT change the
number of sig figs
16) taking measurements: “ ½ the least count”
If a balance measures in grams, estimated figure is ½ gram
17) Calculations using sig figs:
a) A calculated number is precise as the least precise
measurement.
b) The quantity with the fewest number of measured sig
figs determines the sig figs in any calculation.
c) Round off a calculation once, at the end of a problem,
not at every step.
18) Rules for rounding off:
a)
b)
c)
d)
decide how many sig figs
look at next figure that follows
if that figure is ≥ 5 round up
but if is < 5 truncate.
19) Addition and subtraction: answer rounded off
number of decimal places of measurement with fewest
decimal places
20)Multiplication and division:
answer has same number of sig figs as component with
fewest sig figs.
21) US has been slowly adopting metric system since
1893.
History of Metric System
22) Measurements based upon natural world.
23) unit of length = meter = 1m.
24) 1 meter = 1/10,000,000 distance from North Pole to
Equator.
25) Centigrade or Celsius : based upon water.
0oC = freezing point , 100oC = boiling point
26) kilogram = unit of mass, based upon water.
27) one kilogram of water occupies 1 liter.
28) 1 liter = 0.1m X0.1m X 0.1m= 1X10-3 m3
29) we will always use MKS Meters – Kilograms-Seconds
30) prefixes are multiples of 10.
31) convert units using factor label method
Name
Symbol
Giga
G
Mega
M
Kilo
k
Base units: meter , liter , gram , - - - sec
Deci
d
Factor
10
10
10
9
6
3
0
10 = 1
10
-1
Centi
c
Milli
m
Micro
m
nano
n
Pico
p
10
10
10
10
-2
-3
-6
-9
-12
10
32) Using the table: the factor tells you how many prefix
units are equal to 1 base unit.
-9
33)Examples: 1 nanometer = 1 nm = 10 meters
34) use the table to write a ratio between a base unit and
a prefix unit
Multiply straight across and cancel the units
35)example: 260 mm = ? Meters
-2
260 mm X 10 meter = 2.6 m
1 mm
36) Multiple step conversions
prefix1 → base→prefix2