Transcript Significant Figures What is a significant figure?

Significant Figures
What is a significant figure?
• There are 2 kinds of
numbers:
–Exact: the amount of
money in your account.
Known with certainty.
What is a significant figure?
–Approximate: weight,
height—anything
MEASURED. 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
21.7cm.
How do I know how many Sig Figs?
• Rule: All digits are
significant starting with
the first non-zero digit
on the left.
How do I know how many Sig Figs?
• Exception to rule: In
whole numbers that end
in zero, the zeros at the
end are not significant.
How many sig figs?
•7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000
•1
•1
•1
•1
•1
•1
How do I know how many Sig Figs?
nd
•2
Exception to rule: If
zeros are sandwiched
between non-zero digits,
the zeros become
significant.
How do I know how many Sig Figs?
• 3rd Exception to rule: If
zeros are at the end of a
number that has a decimal,
the zeros are significant.
(showing how accurate the
measurement is)
How many sig figs here?
•
•
•
•
•
•
3401
2100
2100.0
5.00
0.00412
8,000,050,000
•
•
•
•
•
•
4
2
5
3
3
6
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
The Distance From the Sun to the
Earth
93,000,000
Step 1
• Move decimal left
• Leave only one number in front of decimal
Step 2
• Write number without zeros
Step 3
• Count how many places you moved decimal
• Make that your power of ten
The power of
ten is 7 because
the decimal
moved 7 places.
• 93,000,000 --Standard Form
• 9.3 x 107 --Scientific Notation
Practice Problem
Write in scientific notation.
Decide the power of ten.
1)
2)
3)
4)
10?
98,500,000 = 9.85 x
64,100,000,000 = 6.41 x 10?
279,000,000 = 2.79 x 10?
4,200,000 = 4.2 x 10?
9.85 x 107
6.41 x 1010
2.79 x 108
4.2 x 106