Transcript Chemistry You Need to Know

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
following
numbers in
scientific
notation.
0.000065423 g
128.90 g
0.0000007532 m
Example #1
Example:
Write the
following
numbers in
scientific
notation.
4
12457.656 m
1.2457656  10 m
0.000065423 g
6.5423  10 g
128.90 g
1.2890  10 g
-5
2
-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
Example:
Write the
following
numbers in
scientific
notation.
4
12457.656 m
1.24567656  10 m
0.000065423 g
6.5423  10 g
128.90 g
1.2890  10 m
-5
2
-7
0.0000007532 m 7.532  10 m
Large original numbers have positive exponents
Tiny original numbers have negative exponents
Reading Scientific Notation
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
the
following
numbers.
2.875  102 g
8.755  10-5 g
7.005 10-3 m
Example #2
Example:
Write out
the
following
numbers.
1.37  104 m
13700 m
2.875  102 g
287.5 g
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
Example:
Write the
following
numbers in
scientific
notation.
with 3 sig digs
0.0002307 m with 2 sig digs
12056.76 mL with 4 sig digs
0.00000024 g with 2 sig digs
Examples #3
with 3 sig digs
1.20 × 105 g
0.0002307 m with 2 sig digs
2.3 × 10-4 m
12056.76 mL with 4 sig digs
1.206 × 104 mL
0.00000024 g with 2 sig digs
2.4 × 10-7 g
120347.25 g
Example:
Write the
following
numbers in
scientific
notation.
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
Example:
Write the
following
numbers in
scientific
notation.
with 2 sig digs
120009.2 m with 3 sig digs
239087.54 mL with 4 sig digs
0.0000078009 g with 3 sig digs
1.34 × 10-3 g
Example:
Write out
the
following
numbers
2.009  10-4 mL
3.987  105 g
2.897  103 m
Let’s Practice
0.0007650 g
Example:
Write the
following
numbers in
scientific
notation.
Example:
Write out
the
following
numbers
with 2 sig digs
7.7 × 10-4 g
120009.2 m with 3 sig digs
1.20 × 105 m
239087.54 mL with 4 sig digs
2.391 × 105 mL
0.0000078009 g with 3 sig digs
7.80 × 10-6 g
1.34 × 10-3 g
0.00134 g
2.009  10-4 mL
0.0002009 mL
3.987  105 g
398700 g
2.897  103 m
2897 m