Download Scientific Notation

Scientific Notation:
A Review
Physics 1st 6wks
How wide is our observable
universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is 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
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
1) 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 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 (aka
“standard”) notation.
0.00018
3) Express 4.58 x 106 in decimal notation.
4,580,000
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
Scientific Notation on the Screen
• When you use the EE feature to input the “x 10” portion of a
scientific notation value in calculator it will be displayed as
Which correctly depicts 0.016 or 1.6 x 10-2
• You can also type “10^” symbol in the calculator to replace the
“x 10” portion and see this instead (but that’s up to you)
• However if you used the ^ symbol by itself, and say this
• You really typed 0.390625 instead of 0.016
4) Use a calculator to evaluate:
4.5 x 10-5
1.6 x 10-2
Type 4.5
-5
1.6
-2
You must include parentheses if you don’t use
those buttons!!
(4.5 x 10
-5)
(1.6 x 10
-2)
0.0028125
Write in scientific notation.
2.8125 x 10-3
5) Use a calculator to evaluate:
7.2 x 10-9
1.2 x 102
On the calculator, the answer is:
6E -11
The answer in scientific notation is
6 x 10 -11
The answer in decimal/standard
notation is
0.00000000006
6) Use a calculator to evaluate
(0.0042)(330,000).
On the calculator, the answer is
1386.
The answer in decimal/standard
notation is
1386
The answer in scientific notation is
1.386 x 103
7) Use a calculator to evaluate
(3,600,000,000)(23).
On the calculator, the answer is:
8.28 E +10
The answer in scientific notation is
8.28 x 10 10
The answer in decimal/standard
notation is
82,800,000,000
Write (2.8 x 103)(5.1 x 10-7) in
scientific notation.
1.
2.
3.
4.
14.28 x 10-4
1.428 x 10-3
14.28 x 1010
1.428 x 1011
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
8) 234.6 x
9
10
2.346 x 1011
9) 0.0642 x 104
6.42 x 10 2
Write 531.42 x 105 in scientific
notation.
1.
2.
3.
4.
5.
6.
7.
.53142 x 102
5.3142 x 103
53.142 x 104
531.42 x 105
53.142 x 106
5.3142 x 107
.53142 x 108
Going from scientific notation to
decimal/standard notation – with a positive
exponent
• When you see a number in scientific notation like
9.87 x 104 the exponent will tell you how many
times to move the decimal to the right to put it back
into decimal notation
• The positive exponent means the number is a “large
number”, that is one that is not less than one.
• Therefore 9.87 x 104 is equal to 98700
Write 8.04 x 105 in decimal notation.
A.
B.
C.
D.
E.
804
8040
80400
804000
8040000
Going from scientific notation to decimal
notation – with a negative exponent
• When you see a number in scientific notation like
9.87 x 10-4 the exponent will tell you how many
times to move the decimal to the left to put it back
into decimal notation
• The negative exponent means it is a “small”
number, that is a number less than one.
• Therefore 9.87 x 10-4 is equal to 0.000987
Write 8.04 x 10-2 in decimal
notation.
A.
B.
C.
D.
E.
804
80.4
0.804
0.0804
0.00804
An interesting situation…
• When you see a number in scientific notation like
9.87 x 100
• The zero exponent means that the decimal point is
not moved at all.
• Therefore 9.87 x 100 is equal to 9.87
• There will virtually never be a reason why we would do that
in Physics since we use Scientific Notation to express large
numbers (especially those with large amounts of zeroes) in
smaller, more manageable forms, but its cool to know it
anyway!