# Chemistry You Need to Know

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```					Section 1.6—Scientific
Notation
Scientific Notation
 Scientific Notation is a form of writing very large
or very small numbers in a faster format
 Scientific notation uses powers of 10 to shorten
the writing of a number.
Writing in Scientific Notation

The decimal point is put behind the first
non-zero number
The power of 10 is the number of times it
moved to get there
A number that began large (>1) has a
positive exponent & a number that began
small (<1) has a negative exponent
Example #1
12457.656 m
Example:
Write the    0.000065423 g
following
numbers in
scientific   128.90 g
notation.

0.0000007532 m
Example #1
4
12457.656 m       1.24567656  10 m
Example:
-5
Write the       0.000065423 g     6.5423  10 g
following
numbers in                                     2
scientific      128.90 g          1.2890  10 g
notation.
-7
0.0000007532 m 7.532  10 m

The decimal is moved to follow the first non-zero number

The power of 10 is the number of times it’s moved
Example #1
4
12457.656 m             1.24567656  10 m
Example:
-5
Write the        0.000065423 g           6.5423  10 g
following
numbers in                                               2
scientific       128.90 g                1.2890  10 m
notation.
-7
0.0000007532 m 7.532  10 m

Large original numbers have positive exponents

Tiny original numbers have negative exponents

A positive power of ten means you need to
make the number bigger and a negative
power of ten means you need to make the
number smaller
Move the decimal place to make the
number bigger or smaller based on the
power of ten
Example #2
1.37  104 m
Example:
Write out   2.875  102 g
the
following
numbers.
8.755  10-5 g

7.005 10-3 m
Example #2
1.37  104 m          13700 m
Example:
Write out        2.875  102 g         287.5 g
the
following
numbers.
8.755  10-5 g        0.00008755 g

7.005 10-3 m         0.007005 m

Move the decimal “the power of ten” times

Positive powers = big numbers. Negative powers = tiny numbers
Scientific Notation & Significant Digits

Scientific Notation is more than just a short
hand.
It is also a more convenient way to look at
our significant digits.
Take a look at this…

Write 120004.25 m with 3 significant digits

120004.25 m             8 significant digits

120000. m               6 significant digits

120000 m                2 significant digits

1.20  105 m            3 significant digits

120. m     Remember…120 isn’t the same as 120000! Just because
those zero’s aren’t significant doesn’t mean they don’t
have to be there! This answer isn’t correct!
Examples #3

120347.25 g   with 3 sig digs
Example:
Write the    0.0002307 m with 2 sig digs
following
numbers in
12056.76 mL with 4 sig digs
scientific
notation.
0.00000024 g with 2 sig digs
Examples #3

120347.25 g       with 3 sig digs       1.20 × 105 g
Example:
Write the        0.0002307 m with 2 sig digs             2.3 × 10-4 m
following
numbers in                                                1.206 × 104 mL
12056.76 mL with 4 sig digs
scientific
notation.
0.00000024 g with 2 sig digs            2.4 × 10-7 g

Move the decimal after the first non-zero number
Start counting significant figures from that first non-zero number
Round when you get the wanted number of significant digits
Remember—large numbers are positive powers of ten & tiny numbers have
negative powers of ten!
Let’s Practice

0.0007650 g     with 2 sig digs
Example:
Write the    120009.2 m with 3 sig digs
following
numbers in
239087.54 mL with 4 sig digs
scientific
notation.
0.0000078009 g with 3 sig digs

1.34 × 10-3 g
Example:
Write out     2.009  10-4 mL
the
following     3.987  105 g
numbers
2.897  103 m
Let’s Practice

0.0007650 g     with 2 sig digs      7.7 × 10-4 g
Example:
Write the    120009.2 m with 3 sig digs           1.20 × 105 m
following
numbers in                                         2.391 × 105 mL
239087.54 mL with 4 sig digs
scientific
notation.
0.0000078009 g with 3 sig digs       7.80 × 10-6 g

1.34 × 10-3 g            0.00134 g
Example:
Write out     2.009  10-4 mL          0.0002009 mL
the
following     3.987  105 g            398700 g
numbers
2.897  103 m            2897 m

```
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