Transcript Significant Figures - (www.ramsey.k12.nj.us).

Significant Figures
What is a significant figure?
There are 2 kinds of numbers:
1. Exact: Known with certainty.
Example: the number of students in
this room
2. 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
• 21.700 cm to a scientist
means the measurement
is accurate to within
1/1000 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 21.7cm.
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 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
4
2
5
3
3
6
What about calculations
with sig figs?
• Rule: 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
round to
 9cm
Multiplication and Division
• Rule: 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 = ?
2
728 cm
Have Fun Measuring
and Happy Calculating!