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Chapter 4: Measurements
and Significant Figures
A significant figure is a digit that
is a reliable indicator of value.
Significant figure conventions guide
us when we report the results of
measurements so that what we
report indicates the exactness of the
measuring device.
Chapter 4: Measurements
and Significant Figures
Chapter 4, Box 1 (p.53)
1. The number of significant
figures is related to the
certainty of a measurement or
a count of great magnitude.
(number of microscopes in lab
vs. number of sand grains on
beach)
Chapter 4, Box 1 (p.53)
2. When reporting a
measurement, record as many
digits as are certain plus one digit
that is estimated.
(with meter or ruler, estimate
last place…..on digital display,
assume instrument estimated last
place)
Chapter 4, Box 1 (p.53)
3. All non-zero digits in a number
are significant.
(98.34 has four significant
figures)
Chapter 4, Box 1 (p.53)
4. All zeros between two nonzero digits are significant
(100.4 has four significant
figures)
Chapter 4, Box 1 (p.53)
5. Zero digits to the right of a
non-zero digit but to the left of
an assumed decimal point may or
may not be significant.
$156,400,000
place holders,
but not significant
figures
Chapter 4, Box 1 (p.53)
6. All zeros to the right of a
decimal point and to the right of
a non-zero digit before a decimal
place are significant.
340.00
0.34000
3.4000
all have five significant figures
Chapter 4, Box 1 (p.53)
7. All digits to the left of a nonzero digit and to the right of a
decimal point are not significant
unless there is a significant digit
to their left.
0.0098
0.4098
two significant figures
four significant figures
Chapter 4, Box 2 (p.55)
1. It is assumed that the last
digit of a result from a
calculation is rounded.
2. When rounding:
a. If the digit to be dropped is
less than 5, the preceding
digit remains the same.
Ex.
54.83 is rounded to 54.8
Chapter 4, Box 2 (p.55)
2. When rounding:
b. If the digit to be dropped is
5 or more, the preceding
digit increases by one.
Ex.
54.78 is rounded to 54.8
Ex.
54.65 is rounded to 54.7
Chapter 4, Box 2 (p.55)
3. Round after performing a
calculation.
4. Rule for addition or subtraction
is different than for multiplication
or division.
Depends on number of places to
the right of the decimal point
Chapter 4, Box 2 (p.55)
4. Rule for addition or subtraction
is different than for multiplication
or division.
Depends on number of places to
the right of the decimal point (least)
98.0008
7.9878
+56.2
162.1886 round to 162.2
Chapter 4, Box 2 (p.55)
5. In multiplication and division,
keep as many significant figures
as are found in the number with
the least significant digits.
0.54678 X 0.980 X 7.899 = 4.23
3 significant
figures
Significant Digits
The “Pacific-Atlantic” Rule for Significant
Digits:
If a decimal is
Present, start
counting from
the Pacific
side
first nonzero digit
1 2 3
0.00650
3 significant
digits
Significant Digits
The “Pacific-Atlantic” Rule for Significant
Digits:
If a decimal is
Absent, start
counting from
the Atlantic
side
5 significant
digits
5 4 32 1
12303000
first nonzero digit