Unit 1 Into to Measurement
Uncertainty in Data
Precision: A reliable measurement will give about
the same results time and time again under the
same conditions. Precision refers to the
reproducibility of a measurement.
 Accuracy: A measurement that is accurate is the
correct answer or the accepted value for the
measurement. High accuracy = close to accepted
value.

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Examples:
 More Examples:
 True Value = 34.0 mL
Measurements = 34.2 mL, 34.1 mL, 34.2
mL
Accurate and/or Precise?
 True Value = 29.3 cm
Measurements = 32.3 cm, 32.5 cm, 32.4
cm
Accurate and/or Precise?
 True Value = 27.3 s
Measurements = 27.9s, 30.2s, 26.9s
Accurate and/or Precise?
Significant Figures
You are often asked to combine measurements
mathematically. When measurements are
combined mathematically, the uncertainty of the
separate measurements must be correctly be
reflected in the final answer.
 A set of rules exists to keep track of the significant
figures in each measurement.
 The significant figures (SIG FIGS) in a
measurement include the certain digits and the
estimated digit of a measurement.

SIG FIG RULES !!

Nonzero numbers are always significant.

Zeros between nonzero numbers are always
significant. Sandwich Zeros


◦ 14 =
◦ 523=
◦ 101
◦ 2005
=
=
◦ 100.0
◦ 2030.0
=
=
Zeros after significant figures are significant only if
they are followed by a decimal point. (All final
zeros to the right of the decimal are significant).
Place holder zeros are NOT significant. To remove
placeholder zeros, rewrite the number in scientific
notation.
◦ 0.001
=
◦ 0.0000034
=
How many sig figs in these
measurements?

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
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

3.4567 = _____
3.00047 = _____
0.00003409 = _____
2.05 X 105 = _____
0.100 = _____
3000 = _____
Sig Figs in Calculations
For multiplication and division: The least number
of sig figs in the measurements determines how
many sig figs in the final answer.
 Ex: 6.15 m x 4.026 m = 24.7599 m2 What is the
fewest # of sig figs? (3) so the answer is rounded
to 24.8 m2
 If a calculation involves several steps, ONLY
ROUND FINAL ANSWER, carry extra sig figs
in intermediate steps. If the digit to be rounded is
less than 5, round down; if 5 or more, round up.


Ex. 24 cm X 32.8 cm = 763.2 cm2

◦ Round 763.2 cm2 to ____________


Ex. 8.40 g 4.2 g/mL = 2 g/mL

◦ 2 g/mL must be rounded to ____________

For addition and subtraction: The sum or
difference has the same number of decimal places
as the measurement with the least number of
decimal places.

EX: 951.0g + 1407 g + 23.911 g + 158.18 g =
2540.091 g But the measurement with the fewest
places past decimal is 1407 g ( It has no digits
past decimal) SO the final answer must be
rounded to 2540. g

Ex.
49.1 g + 8.001 g = 57.101 g

◦ Round the answer to ___________


Ex.
81.350 m – 7.35 m = 74 m

◦ Round the answer to ____________
Percent Error
Percent error compares a measurement with its
accepted value. A percent error can be either positive
or negative.
 % ERROR = measured - accepted
x 100
accepted


% ERROR = what you got – what is correct
what is correct
x 100
Scientific Notation
Some measurements that you will encounter in
physics can be very large or small. Using these
numbers in calculations is cumbersome. You can
work with these numbers more easily by writing
them in scientific notation. A number written in
scientific notation is written in the form
 M X 10n
 Where M is a number between 1 and 10 (known as
the coefficient) and 10 is raised to the power of n
(known as the exponent). Circle the numbers that
are in correct scientific notation:



1 X 104
12 X 1012
2.54 X 10-3
0.9 X 103
9.99 X 102

Step 1: Determine M by moving the decimal
point in the original number to the left or right so
that only one nonzero digit is to the left of the
decimal….do it!!!

27508.

Step 2: Determine “n” , the exponent of 10, by
counting the number of decimal places the
decimal point has moved. If moved to the left, n
is positive. If moved to the right, n is negative.

2.7508
4 places to the left, n = 4
Answer = 2.7508 X 104

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
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
Write the following quantities in scientific
notation…do it!!!
0.0050 =
235.4 =
18,903 =
0.0000101 =
Write the following quantities in arithmetic
notation…do it!!!
1.45 X 104 =
2.34 X 10-3
6.02 X 1023 =
Units and Measurements
The International System of measurement or
“metric” system is the preferred system.
 Make sure you are familiar with the basic units that
we will be using many times throughout the year.

Quantity
Unit
Abbreviations
Time
Second
s
Length
Meter
m
Mass
Gram
g
Temperature
Kelvin
K
Make sure to be familiar with the common prefixes
that make the base unit larger (kilo- for example) and
prefixes that make the unit smaller ( examples milli and centi-)
 You should know how to quickly change between the
units, for example, from liter to milliliter or kilograms
to grams.
Prefix
Symbol

Kilo
k.
Hecta
h.
Deca
da
Base Unit
Deci
d
Centi
c
Milli
m
Factor Label/ Dimensional Analysis
Dimensional Analysis: A technique of converting
between units.
 Dimensional analysis use conversion factors. A
conversion factor is always equal to 1. For
example: 1000mor 60 minute
1 km
1 hour
 Conversion factors can be flipped to allow for
cancellation of units.
 Choosing the correct conversion factors requires
looking carefully at the problem.


Step 1: Show what you are given on the
left, and what units you want on the right.

Step 2: Insert the required conversion
factor(s) to change between units. In this
case we need only one conversion factor,
and we show it as a fraction, 1 hr/60 min.
We put units of minutes on the bottom so
they will cancel out with the minutes on
the top of the given.

Step 3: Cancel units where you can, and
solve the math.
For example let’s look at the following question:
 Example 1: Given that there are
5280feet in a mile, How many feet are in
2.78 miles?


Example 2: Convert 89 km into inches

Example 3: How many gallons are in 146
Liters? 1 Gal= 4 quarts
1 L = 1.057
quarts
1 L=1000ml

Example 4: How many seconds in 5.00 days?