Download Scientific Notation

Scientific Notation
What is it?
How do I use it?
Why?!?!?!
Scientific Notation
• Scientific notation, also called power-of-10 notation,
is a method of writing extremely large and small
numbers.
• Scientific notation makes it easy to multiply and
divide gigantic and/or very small numbers.
• For very large or very small numbers, it is sometimes
simpler to use "scientific notation" (so called, because
scientists often deal with very large and very small
numbers).
• The format for writing a number in scientific notation
is fairly simple: first digit of the number followed by
the decimal point and then all the rest of the digits
of the number, times 10 to an appropriate power.
Scientific Notation
• A number is in Scientific Notation if:
–
–
–
–
It is in the form of a x 10b
a is a decimal.
1< a <10
b is an integer
Determine if each of the following is in proper
Scientific Notation form. Be prepared to
support your answer.
Problem:
Response:
Reason:
1. 3 x 102
2. 0.4 x 102
3. 35 x 102
4. ½ x 102
5. 4.0 x 101/2
6. 3.5 x 10-4
Compare your answers with the
table below.
Problem:
Response:
Reason:
1. 3 x 102
YES
Follows all rules.
2. 0.4 x 102
NO
Decimal part is less
than 1.
3. 35 x 102
NO
Decimal part is
greater than 10.
4. ½ x 102
NO
Decimal part is not a
decimal and it is less
than 1.
5. 4.0 x 101/2
NO
Exponent is not an
integer.
6. 3.5 x 10-4
YES
Follows all rules.
To write a number in Scientific Notation:
Step 1:
• Find the original decimal point, label the
decimal point “old”. What if there is not a
decimal point? Where is it?
.000054
old
43.56
old
4,560,000,000
old
To write a number in Scientific Notation:
Step 2:
• Start on the left and put a new decimal point after
the first digit that is NOT a zero. Label this decimal
point “new”. Write this number down in front of the x
10.
.000054
43.56
4,560,000,000
.00005.4
4.3.56
4.560,000,000
old
new
5.4 x 10
new
old
4.356 x 10
new
4.6 x 10
old
To write a number in Scientific Notation:
Step 3:
• Count the number of spaces from the
new to the old decimal point. This is
your exponent. Decimal x 10
Think of a number line, if you count the right, the exponent will be
positive, to the left negative.
new
old
old
new
old
new
.000054
5…4….3….2……1
1
Counted left,
exponent negative.
5.4 x 10
4.3.56
-5
Counted right,
exponent positive.
4.356 x 10 1
4.560,000,000
1…..2....3…..4……5..6……7…..8….
Counted right,
exponent positive.
4.56 x 10
9
9
To write a number in Scientific Notation:
Final Answers
.000054
5.4 x 10
5
43.56
4.356 x 10 1
4,560,000,000
4.56 x 10
9
Let’s Practice!
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•
•
•
•
•
•
Directions: Label the new and the old decimals. Write in Scientific
Notation, OR write the number in standard notation.
5,760,000,000
0.00000765
4.5 x 108
3.8 x 10-5
6,798,000
1.34 x 106
0.000945
•
•
•
•
•
•
•
5.76 x 109
7.65 x 10-6
450,000,000
0.000038
6.798 x 106
1,340,000
9.45 x 10-4