Transcript Significant Figures - Mr. Saunders` Science

“A man with a watch knows
what time it is. A man with two
watches is never sure”
(Unknown)
Significant Figures
Physical Science
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.
How do I know how many Sig Figs?
• 3rd Exception to rule:
These zeros are showing
how accurate the
measurement or
calculation are.
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 off 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
• Round to
 139cm2
• 75.8cm x 9.6cm = ?
2
cm
The End
Have Fun Measuring and
Happy Calculating!
How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal
notation. When numbers get this large,
it is easier to write them in scientific
notation.
Scientific Notation
A number is expressed in scientific
notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
Write the width of the universe in
scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make
this number be between 1 and 10?
Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the
decimal?
23
When the original number is more than 1,
the exponent is positive.
The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 10?
9.02
The decimal was moved how many places?
8
When the original number is less than 1, the
exponent is negative.
9.02 x 10-8
Write 28750.9 in scientific notation.
1.
2.
3.
4.
2.87509 x 10-5
2.87509 x 10-4
2.87509 x 104
2.87509 x 105
2) Express 1.8 x 10-4 in decimal
notation.
0.00018
3) Express 4.58 x 106 in decimal notation.
4,580,000
On the graphing calculator, scientific
notation is done with the
button.
4.58 x 106 is typed 4.58
6