Download Circle the numbers that are correctly written in

Scientific Notation
Created by Patrick Haney
Scientific Notation (S.N.) is a way
to look at numbers that are very
large in magnitude or very small in
magnitude.
2570000000000 = 2.57 × 1012
0.000000000125 = 1.25 ×
-10
10
When you see a number in scientific
notation, it is NOT an equation. It is an
alternative way to write a number.
There are two things that are always true
of a number written in scientific notation:
1. There is always one non-zero number in front
of the decimal when a number is written in S.N.
2. The number is always multiplied by 10b,
where b is an integer.
Understanding what we mean:
1. There is always one non-zero number in front
of the decimal when a number is written in S.N.
Which numbers below are correctly written
in scientific notation?
3.5 × 1016
16.4 × 10-11
1.34 × 1014
10.7 × 10-24
2.44 × 1021
0.2 × 1010
Understanding what we mean:
2. The number is always multiplied by 10b,
where b is an integer.
Which numbers below are correctly written
in scientific notation?
1.5 × 10-1.6
7.2 × 10-11
9.25 × 1014
5.20 × 10-21
3.24 × 102.5
8.3 × 101.25
Circle the numbers that are correctly
written in scientific notation and place
an X over the numbers that are not.
Understanding when to use positive or negative
exponents:
Which number written in scientific notation
correctly represents the number below?
218000000000
2.18 × 1011
OR
2.18 × 10-11
0.000000000000145
1.45 × 1013
OR
1.45 × 10-13
Which number written in scientific notation correctly
represents the number below?
0.000000000287
2.87 × 1010
OR
2.87 × 10-10
96810000000000000
9.681 × 1016
OR
9.681 × 10-16
62000000000000
6.2 × 1013
OR
6.2 × 10-13
Which number written in scientific notation correctly
represents the number below?
0.000000000129
1.29 × 1010
OR
1.29 × 10-10
0.00000000301
3.01 × 109
OR
3.01 × 10-9
120600000000000
1.206 × 1014
OR
1.206 × 10-14
Describe what a positive and negative
exponent means:
A positive exponent means that the
number is very large in magnitude.
Example: 27500000000000
A negative exponent means that the
number is very small in magnitude.
Example: 0.000000000000275
Understanding this simple concept will keep you from
having to memorize whether the decimal should move to
the left or the right!
For each of the numbers
on your notes, select the
correct representation
written in scientific
notation.
Which number below is the same as the number
written in scientific notation?
1.26 × 1012
1260000000000
OR
0.00000000000126
2.05 × 1010
20500000000
OR
0.000000000205
5.61 × 10-9
5610000000
OR
0.00000000561
Which number below is the same as the number
written in scientific notation?
7.35 × 108
OR
735000000
0.0000000735
8.05 × 10-10
80500000000
OR
0.000000000805
1.3 × 10-11
130000000000
OR
0.000000000013
Putting a number into scientific notation:
Because the number below is of a large magnitude,
positive
the exponent will be ___________.
Count the number of times the decimal moves.
2.8.0.0.0.0.0. 0. 0. 0.
In scientific notation this number is 2.8 × 109
Putting a number into scientific notation:
Because the number below is of a small magnitude,
negative
the exponent will be ___________.
Count the number of times the decimal moves.
0.0.0.0.0.0.0. 1.2 5
In scientific notation this number is 1.25 × 10-7
Write each of the
numbers on your
notes page in
scientific notation
correctly.
Putting a number
into the calculator in
scientific notation.
If you do not put in
these numbers
correctly, you will
often come out with
the wrong answer.
Example:
6.02 × 1023
Step #1
Put the first number,
call the significand,
into the calculator.
6.02
Example:
6.02 × 1023
Step #2
Press the
key
Step #3
Press the
key
Example:
6.02 × 1023
Step #4
Type in the exponent.
23
This is what it will look like on your screen:
But remember that it means:
6.02 ×
23
10
Translate the numbers on your notes
from how they appear on the calculator
screen to how they should really be
written.
3.01 ×
7.4 ×
24
10
25
10
1.51 ×
1.64 ×
24
10
-27
10
When you place numbers into the
calculator correctly, multiplying
and dividing them is just as easy as
any other numbers.
Practice multiplying and dividing
the numbers in scientific notation
on your notes.
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