Scientific Notation
Review
Physics – 1st Six Weeks
What the TEKS say…
§112.39. Physics
(c) Knowledge and skills.
(2) Scientific processes. The student uses a systematic
approach to answer scientific laboratory and field
investigative questions. The student is expected to:
(H) make measurements with accuracy and precision and
record data using scientific notation and International
System (SI) units
An appetizer to start…
Why do scientists use Scientific
Notation?
Example A:
The width of the observable universe is approximately
210,000,000,000,000,000,000,000 miles
(22 zeros)
Example B:
The diameter of a hydrogen nucleus is approximately
0.00000000000000175 meters
(14 zeroes after the decimal)
If you had to use either value it would be very easy to mistakenly leave a zero off or to ad an
extra zero. Doing so would change the value by a factor of 10. It would be as if your boss handed
you your paycheck for $1000 and it mistakenly was printed for $100. One zero makes a lot of
difference
Decimal Notation aka Standard Notation
Example A:
The width of the observable universe is approximately
210,000,000,000,000,000,000,000 miles
(22 zeros)
Example B:
The diameter of a hydrogen nucleus is approximately
0.00000000000000175 meters
(14 zeroes after the decimal)
These numbers are written in decimal or standard 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 𝟏𝟎 > 𝒂 ≥ 𝟏
and n is an integer
•
Note: when coverting from standard notation to scientific notation,
the “a” value will contain any “sandwiched” zeroes that exist
•
For example these sandwiched zeroes: 4005000000 will be
preserved as 4.005 x 109
Scientific Notation
• For a large number, the integer shows
how many powers of 10 there are.
• For example in 2 x 102 this is the same
as saying 2 x 10 x 10 or 200
• When the integer is positive it tells us
how many places the decimal has
moved to the right of the “a” value
From Scientific to Standard Notation
• Remember: when the integer is positive
it tells us how many places the decimal
has moved to the right of the “a” value
• So 4.58 x 106 in decimal notation is…
4,580,000 since 106 means
4.58
1
2
3 4 5
6
Scientific Notation
• For a small number, the integer shows how
1
many divisions of 10 (or ) there are.
10
• For example in 2 x 10-2 this is the same as
1
1
saying 2 x x or 0.02
10 10
• When the integer is negative it tells us how
many places the decimal has moved to the
left of the “a” value
From Scientific to Standard Notation
• Remember: when the integer is negative
it tells us how many places the decimal
has moved to the left of the “a” value
• So 1.8 x 10-4 in decimal (aka “standard”)
notation is…
• 0.00018 since 10-4 means
1.8
4
3
2
1
Write 9.3 x 104 in decimal (or standard) notation.
A.
B.
C.
D.
E.
93000
9300
930
93
9.3
Write 8.04 x 10-2 in decimal (or standard)
notation.
A.
B.
C.
D.
E.
804
80.4
0.804
0.0804
0.00804
Converting from Standard to Scientific Notation
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 the a comply with 𝟏𝟎 > 𝒂 ≥ 𝟏?
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
Converting from Standard to Scientific Notation
• Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number before the
power of ten be 𝟏𝟎 > 𝒂 ≥ 𝟏?
(Note: Preserve all non-zero numbers as well as any
sandwiched zeroes between them)
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 0.0000705 in scientific notation.
A.
B.
C.
D.
7.05 x 10-4
7.05 x 10-5
7.05 x 104
7.05 x 105
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
Entering Scientific Notation Values on the Calculator
On the graphing calculator, scientific
notation is done by hitting the
button
then the
button (some have their
own button
4.58 x 106 is typed 4.58
6
How Scientific Notation is displayed on the TI Calculator
On the calculator
3500000 would be
displayed in scientific
notation as 3.5E6
It leads to problems!
Use a calculator to evaluate:
4.5 x 10-5
1.6 x 10-2
A.
B.
C.
D.
E.
0.0028125
0.000028125
0.00324
8675309
867.5309
Use a calculator to evaluate
(4.2 x 10-3)(3.3 x 105)
A.
B.
C.
D.
0.001386
404
1386
0.0000404