Name:
Period:
Chapter 3: Scientific Measurement - Sections 3.1 - 3.3 notes
Qualitative: A non-numerical
or
of something. (quality) Does
not involve
e.g. “The liquid boiled and formed a gas.”
Quantitative: An observation that involves
e.g.
“The liquid boiled at 105 degrees Celsius”
(quantity).
Accuracy: How close a measurement is to the
measurement.
for that
Precision: How
a group of measurements are to each other. Shows if
the measurement is
?
Drawing (arrows and target):
Error and Percent Error:
Error = Accepted Value – Experimental Value
Percent Error =
| Accepted Value – Experimental Value | x 100
Accepted Value
Example:
Scientific Notation: A method of expressing
or
numbers
A number written in scientific notation consists of two parts:
•a
which is   1 and  10
• an
(a power of 10)
2300 = 2.3 x 103
The coefficient is
The exponent is
2300 = 2.3 x
Examples:
x
x
12 000 000 =
0.00356 =
85 130 =
0.000 05 =
0.0342 =
602 200 000 000 000 000 000 000 =
1
Name:
Period:
Interpreting Powers of Ten:
103
= thousand
= thousandth
10-6
= million
9
10
= millionth
= billion
= billionth
10-12
= trillion
= trillionth
Multiplying using scientific notation requires 3 steps:
1)
the coefficients together
2)
the exponents
3)
Adjust the coefficient of the answer so that it is
necessary.
Examples:
, if
(3 x 104) x (2 x 10 2) =
(3.5 x 106) x (4.0 x 1012) =
(2.1 x 103) x (5.0 x 107) =
Dividing using scientific notation requires 3 steps:
1)
one coefficient by the other
2)
the exponents
3)
Adjust the
of the answer so that it is
, if necessary.
Example:
3.0 x 105 / 6.0 x 102 =
Addition and Subtraction using Scientific Notation
Before numbers can be added or subtracted, the
must be the
.
(6.6 x 10 -8) + (4.0 x 10-9) =
`
(3.42 x 10 -5) – (2.5 x 10-6) =
Significant Figures
Why is there uncertainty in measurements?
Because all measurements are done with
can read to an
and no instrument
number of decimal places.
You need to know three things about significant figures:
• what significant figures are
• how to recognize which of the figures in a measurement are significant and which are not
• how to do calculations using measurements and determine the correct # of sigfigs
2
Name:
Period:
Significant Figures: All digits in a measurement that are certain, plus one
digit.
Rules for Determining the Number of Sigfigs
1) All
numbers are significant.
Examples:
12.39 mL
5689.751 g
2) All “captured” zeros are
Examples:
3) “Leading” zeros are
Examples:
sigfigs
sigfigs
.
1304.5 cm
53000.004 m
sigfigs
sigfigs
significant. (They are often important as
, but are not as part of the measurement)
00000435 g
0.000435 g
4.35 x 10-4 g
sigfigs
sigfigs
sigfigs
4) “Trailing” zeros are significant iff a
Examples:
14.600 mL
14.60 mL
500
g
500.
g
500.000 g
0.000 125 30 L
0.340 000 00 m
is present.
sigfigs
sigfigs
sigfigs
sigfigs
sigfigs
sigfigs
sigfigs
Remember: Sigfigs deal ONLY with measurements;
numbers of sigfigs.
have infinite
e.g. 45 cows is the same as 45.000000000000… cows
However, if the mass of the 45 cows was 10227.0 kg then that
have 6 sigfigs.
Metric
would
numbers also have infinite numbers of sigfigs;
1 meter = 100.00000000000… centimeters
1 milliliter = 0.001000000000…liters
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Name:
Period:
Using Sigfigs in Calculations Involving Measurements
Just as a chain is only as strong as its
link, so a calculation using
measurements is only as accurate as its
measurement
A quick reminder about Rounding
 Determine how many
 Locate that final digit by counting from the
 Is the next digit to the right less than 5?

 Is the next digit to the right 5 or greater?

are needed
to the final digit
the final digit by 1
a) 314.721 meters (four)
b) 0.001775 meter (two)
c) c) 8792 meters (two)
When multiplying or dividing with measurements, the answer will have the same number of
as the
Examples:
measurement.
6.38 cm x 2.0 cm = 12.76 cm2
1.400 m2 ÷ 0.00244 m = 573.7704918 m
(2.000 x103 cm2) x ( 45.9230cm) = 91846 cm3
When adding and subtracting with measurements, the answer will have the same number of
as the measurement with the
of decimal places.
Examples:
6.8 cm + 11.934 cm = 18.734 cm
14.966 ºC + 126. ºC = 140.966º C
4