Download Significant Figures - Ramsey Public School District

SIGNIFICANT
FIGURES
What is a significant figure?
There are 2 kinds of numbers:
1.
2.
Exact: Known with certainty.
Example: the number of students in this
room
Approximate: anything MEASURED.
Example: Mass, volume, length, weight,
height
No measurement is perfect.
When to use Significant figures
When a measurement is
recorded only those digits that
are dependable are written
down.
When to use Significant figures
If you measured the width of a
paper with your ruler you
might record 21.7cm.
To a mathematician 21.70, or
21.700 is the same.
But, to a scientist 21.7cm and 21.70cm
is NOT the same
21.700cm to a scientist means
the measurement is accurate
to within one thousandth of a
cm.
But, to a scientist 21.7cm and 21.70cm
is NOT the same
If you used an ordinary ruler, the
smallest marking is the mm, so
your measurement has to be
recorded as 21.70cm.
How do I know how many Sig Figs?
Rule 1: All non zero digits are
significant.
Example: 1,246 (4 sig figs)
How do I know how many Sig Figs?
Rule 2: Any zeros between
significant digits are also
significant.
Example: 1,206 (4 sig figs)
How do I know how many Sig Figs?
Rule 3: If the number does not
contain a decimal point, any
zeros to the right of a nonzero
number are NOT significant
Example: 1,200 (2 sig figs)
How do I know how many Sig Figs?
Rule 4: If zeros are at the end of a
number that has a decimal, the
zeros are significant.
Example: 1,200. (4 sig figs)
How do I know how many Sig Figs?
Rule 5: If a value has no significant
digits to the left of a decimal point,
any zeros to the right of the decimal
point before the non zero numbers
(leading zeros) are not significant.
Example: 0.0012 (2 sig figs)
How do I know how many Sig Figs?
Rule 6: Zeros that are found after
non zero numbers to the right of a
decimal point are significant
(trailing zeros)
Example: 0.1200 (4 sig figs)
How do I know how many Sig Figs?
When using scientific notation, all of the
sig figs and ONLY the sig figs appear in
the coefficient.
1.00 x 105 has 3 sig figs
How many sig figs?
7
40
0.5
0.00003
7 x 105
7,000,000
1
1
1
1
1
1
How many sig figs here?
1.2
2100
56.76
4.00
0.0792
7,083,000,000
2
2
4
3
3
4
How many sig figs here?
3401
2100
2100.0
5.00
0.00412
8,000,050,000
6.02 x 10-23
4
2
5
3
3
6
3
What about calculations with sig figs?
Rule: Addition/Subtraction
When adding or subtracting
measured numbers, the answer
can have no more places after
the decimal than the LEAST of the
measured numbers.
Add/Subtract examples
2.45cm + 1.2cm = 3.65cm
round to
= 3.7cm
7.432cm + 2cm = 9.432 cm
round to
 9cm
Multiplication and Division
Rule: multiplication/division
When multiplying or dividing,
the result can have no more
significant figures than the
least reliable measurement.
A couple of examples
56.78 cm x 2.45cm = 139.111 cm2
round to
 139cm2
75.8cm x 9.60cm = ?
728 cm2
Have Fun Measuring
and Happy Calculating!