Download Scientific Notation

Scientific Notation
Scientific Notation is used to express the very large
and the very small numbers so that problem solving
will be made easier.
Examples:
The mass of one gold atom is
.000 000 000 000 000 000 000 327 grams.
One gram of hydrogen contains
602 000 000 000 000 000 000 000 hydrogen atoms.
Scientists can work with very large and
very small numbers more more easily if
the numbers are written in scientific
notation.
Objective
The student will be able to:
express numbers in scientific and
decimal notation.
Designed by Skip Tyler, Varina High School
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
If a number is greater than
10, the exponent will be
positive
_____________
and is equal
to the number of places the
decimal must be moved to
left
the ________
to write the
number in scientific
notation.
If a number is less than 10,
the exponent will be
negative
_____________
and is equal
to the number of places the
decimal must be moved to
right
the ________
to write the
number in scientific
notation.
To write a number in scientific notation:
1. Move the decimal to the right of the
first non-zero number.
2. Count how many places the decimal
had to be moved.
3. If the decimal had to be moved to the right,
the exponent is negative.
4. If the decimal had to be moved to the left,
the exponent is positive.
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
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
Practice Problems
Put these numbers in scientific notation.
PROBLEMS
1) .00012
2) 1000
3) 0.01
4) 12
5) .987
6) 596
7) .000 000 7
8) 1,000,000
9) .001257
10) 987,653,000,000
11) 8
ANSWERS
1) 1.2 x 10-4
2) 1 x 103
3) 1 x 10-2
4) 1.2 x 101
5) 9.87 x 10-1
6) 5.96 x 102
7) 7.0 x 10-7
8) 1.0 x 106
9) 1.26 x 10-3
10) 9.88 x 1011
11) 8 x 100
EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
1) 4.9 X 102
1) 490
2) 3.75 X 10-2
2) .0375
3) 5.95 X 10-4
3) .000595
4) 9.46 X 103
4) 9460
5) 3.87 X 101
5) 38.7
6) 7.10 X 100
6) 7.10
7) 8.2 X 10-5
7) .000082
Brain Break
Using the Exponent Key
on a Calculator
EE
EXP
EE or EXP means “times 10 to the…”
How
How to
to type
type out
out 6.02
6.02 xx10
102323::
6
0
.
2
EE
2
3
Don’t do it like this…
6
WRONG!
0
.
yx
2
2
3
…or like this…
6
.
0
WRONG!
2
x
1
…or like this:
6
.
0
0
EE
2
3
TOO MUCH WORK.
2
x
1
0
yx
2
3
How to Use a Scientific Calculator
Divide: (5.44 x 107) .. (8.1 x 104)
07
04
671.604938
5.44
8.100
54400000.
How to enter this on a calculator:
5.44
EE
7
..
8.1
EE
4
8.1
EXP
4
ENTER
OR
5.44
EXP
7
..
671.6049383
rounded to 6.7 x 102
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52
=
1.2 x 105
Example:

2.8 x 1013
Type this calculation in like this:
1
.
2
EE
5
2
.
8
EE
1

3
=
Calculator gives… 4.2857143 –09
or… 4.2857143 E–09
This is NOT written… 4.3–9
But instead is written… 4.3 x 10–9
or
4.3 E –9
7.5 x 10-6  - 8.7 x 10-4 = -6.525 x 10-9
report -6.5 x 10-9 (2 sig. figs.)
4.35 x 106  1.23 x 10-3
= 5.3505 x 103 or 5350.5
report 5.35 x 103 (3 sig. figs.)
5.76 x 10-16  9.86 x 10-4
= 5.84178499 x 10-13
report 5.84 x 10-13 (3 sig. figs.)
8.8 x 10  3.3 x 10
11
11
= 2.904 x 1023
report 2.9 x 1023 (2 sig. figs.)
6.022 x 1023  - 5.1 x 10-8 = -3.07122 x 1016
report -3.1 x 1016 (2 sig. figs.)