Transcript Section 1.6 Scientific Notation

Section 1.6—Scientific
Notation
Scientific Notation
 Scientific Notation is a form of writing very large
or very small numbers that you’ve probably used
in science or math class before
 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
1.24567656  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
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 the number of
times of 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 m
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.
Sometimes there isn’t a way to write a
number with the needed number of
significant digits
…unless you use scientific notation!
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
120347.25 g
Example:
Write the
following
numbers in
scientific
notation.
with 3 sig digs
1.20 × 105 g
0.0002307 m with 2 sig digs
2.3 × 10-4 g
12056.76 mL with 4 sig digs
1.206 × 104 g
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
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
7.6 × 10-4 g
120009.2 m with 3 sig digs
1.20 × 105 g
239087.54 mL with 4 sig digs
2.391 × 105 g
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
Chapter 1—Scientists’ Tools
Summary
Chemistry is an Experimental Science
 You have learned the following:
Common characteristics of scientific processes
How observations & measurements are taken
accurately & precisely during those scientific processes
How to design a lab yourself to answer questions
How to convert units you’ve measured in to ones that
are more useful to calculate with
How to report answers to calculations with the correct
number of significant digits to represent the accuracy of
the measurements you took in the lab
How to use scientific notation to express the correct
number of significant figures
What did you learn about
Scientists’ tools?
Chemistry is an Experimental Science
Although no
one method,
there are
Are used
when you
Design your
own labs
Common
characteristics
Unit
conversions
May require
include
Careful
observation
s
Accurate &
precise
measurements
Scientific
Notation
May require using
When using in
calculations, follow
Significant
digit rules