# Scientific Notation

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Scientific Notation - LARGE Numbers - POSITIVE Exponents
Your pencil has 602,200,000,000,000,000,000,000 carbon atoms.
this number in scientific notation.
Write
Remember, every whole
number has a imaginary
decimal point at the end.
602,200,000,000,000,000,000,000 •
+23
6•0 2 2 x 1 0
1. Find the first non-zero number ...
BASE
NUMBER
x
POWER
OF TEN
... and the last non-zero number.
2. Write that number underneath.
3. Put a decimal after the first digit (6).
6.022 x 10
atoms.
23
* This is the BASE
NUMBER
4. Multiply the base number by the POWER OF TEN
.
5.
Count the number of decimal places from your
NEW decimal point
6.
to your
OLD decimal point.
Write that number as an exponent of 10.
Scientific Notation - SMALL Numbers - NEGATIVE Exponents
Express in scientific notation.
0.0000000005 •
–10
x 10
5
1. Find the first non-zero number ...
... and the last non-zero number.
2. Write that number underneath.
3. Put a decimal after the first digit (5).
* This is the BASE
Since it’s just
a whole
number, get
rid of the
decimal.
NUMBER
It’s
negative
because
the
number
is really
small.
4. Multiply the base number by the POWER OF TEN
5.
Count the number of decimal places from your
NEW decimal point
6.
to your
OLD decimal point.
Write that number as an exponent of 10.
an atom is
5 x 10
-10
m.
Changing
Scientific
--> Standard
Form
WritingNotation
Numbers in Standard
Form
EXAMPLE
2
Convert each value from scientific to standard notation
7 000
x 10
3
1. The exponent will tell you how
many spaces to move the decimal.
Remember, every number
has an imaginary decimal
point after it.
7 0 0 0
4.398
x 10
8
–4
2. Since the exponent is +3
–7 ,move
+8
the decimal 4
7
83 spaces to the right.
left
439,800,000
6.001 x 10
–4
.0 0 0 6001
3 x 10
.0 0 0 0 0 0 3
–7
3. Fill the empty place values with zeros.
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Number theory

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