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SI units and Sig. Figs.
measurement
SI (système internationale)
Physical
Quantity
Unit
Symbol
Volume
Cubic Metre
(litre)
m3
Length
Metre
m
Mass
Kilogram
kg
Time
Second
s
Temperature
Kelvin
K
Amount of substance
Mole
mol
Electric current
Ampere
A
Luminous intensity
Candela
cd
Scientific Notation
Scientists have developed a shorter
method to express very large numbers.
Scientific Notation is based on powers of
the base number 10.
Scientific notation
123,000,000,000 in s.n. is 1.23 x 1011
The first number 1.23 is called the coefficient. It
must be between 1 - 9.99
The second number is called the base . The
base number 10 is always written in exponent
form. In the number 1.23 x 1011 the number 11 is
referred to as the exponent or power of ten.
This large number only has 3 significant digits
To write a large number in
scientific notation:
ex: 36 000
First put the decimal after the first digit and
drop the zeroes. Ex: 3.6
Next, count the number of places from the
decimal to the end of the number. Ex: 4
Finally, put it together. Ex: 3.6 x 104
36 000 only has two significant digits
To write a small number in s.n.
ex: 0.03064
First move the decimal after the first real
number and drop the zeroes. Ex: 3.064
Next, count the number of places moved
from the original decimal spot to the new
decimal spot. Ex: 2
Numbers less than 1 will have a negative
exponent. Ex: -2
Finally, put it together. Ex: 3.064 x 10-2
0.03064 has four significant digits
Precision: to describe
how well a group of
measurements made
of the same object or
event under the same
conditions actually do
agree with one
another.
These points are
precise with one
another but not
accurate.
Accuracy: represents
the closeness of a
measurement to the
true value.
Ex: the bulls-eye
would be the true
value, so these points
are accurate.
Why Significant Figures?
When we take measurements or make
calculations, we do so with a certain
precision. This precision is determined by
the instrument we use to take those
measurements. So, when we do
calculations based on our measurements,
the calculations must be only as precise
as the measurements.
Using sig figs: The Rules!
487
All significant
1. Digits from 1-9 are always significant.
2. Zeros between two other significant digits
2002
are always significant
All significant
3. One or more additional zeros to the right of
both the decimal place and another
significant digit are significant. 6.00
All significant
4. Zeros used solely for spacing the decimal
point (placeholders) are not significant.
47 000
Only two
significant
digits
EXAMPLES # OF SIG.
DIG.
453kg
3
5057L
4
5.00
3
0.007
1
COMMENT
All non-zero digits are
always significant.
Zeros between 2 sig.
dig. are significant.
Additional zeros to the
right of decimal and a
sig. dig. are significant.
Placeholders are not sig.
Problems: Indicate the number of
significant figures...
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.235
2.90
0.0987
0.450
5.00
2300
230
230.0
9870345
1.00000
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Multiplying and Dividing
RULE: your answer may only show as
many sig figs as the multiplied or
divided measurement showing the least
number of significant digits.
Example: 22.37 cm x 3.10 cm = 69.3 only
3 sig figs allowed.
Multiplying and Dividing Practice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
42.3 x 2.61
32.99 x 0.23
46.1 ÷ 1.21
23.3 ÷ 4.1
0.61 x 42.1
47.2 x 0.02
47.2 ÷ 0.023
100 x 23
120 ÷ 0.12
120 x 12 ÷ 12.5
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Adding and Subtracting:
RULE: your answer can only show as
many decimal places as the
measurement having the fewest
number of decimal places.
Example:
3.76 g + 14.83 g + 2.1 g = 20.7 g
Adding and Subtracting Practice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2.634 + 0.02
2.634 - 0.02
230 + 50.0
0.034 + 1.00
4.56 - 0.34
3.09 - 2.0
349 + 34.09
234 - 0.98
238 + 0.98
123.98 + 0.54 - 2.3
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