Write the following numbers in scientific notation:
0.000412
Prefix
Symbol
Scientific Notation
143.0
giga
G
109
mega
M
106
12 000 000 000
Kilo
Convert the following:
1 μm =
m
0.001 A = mA
1hm =
m
k
103
hecto
h
102
deca
da
101
Base unit [gram (g), meter(m), liter (l), etc.] x100
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
Answers
Write the following numbers in scientific notation:
Prefix
Symbol
Scientific
0.000412 => 4.12 x 10 -4
Notation
2
143.0 => 1.43 x 10
giga
G
10
M
10
12 000 000 000 => 1.2 x 1010 mega
9
6
Kilo
Convert the following:
1 μm =
0.000001 m
0.001 A = 1mA
1hm =
100 m
k
103
hecto
h
102
deca
da
101
Base unit [gram (g), meter(m), liter (l),
etc.] x100
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
RULES
Rule 1: All nonzero numbers are significant.
Examples: 4328, 38273, 1234
Rule 2: All zeros that are “sandwiched” or between
two nonzero numbers are significant.
Examples: 303, 23903, 9401
Rule 3: Trailing zeros are significant if the number
contains a decimal.
Examples: 1290.0, 10890. , 10. , 3000.
Not examples: 10, 3000, 870
Rule 4: Leading zeros that function only to hold the
decimal point are NOT significant.
Example: 0.009, 0.65
Rule 5: Zeros that are in a decimal number that are
after a nonzero digit are significant.
Examples: 0.906, 0.8370
Rule 6: If a number is written in scientific notation then
all numbers to the left of the multiplication sign are
significant.
Examples: 1.03 x 102
Let’s Talk About Rounding
What if I have the number 245 200 000 and I want it written with only
3 significant figures.
Which digit would I have to round?
What are the rules of rounding?
Rule 1: If the digit you are rounding is followed by a 0, 1, 2, 3, or 4
then the digit you are rounding stays the same. All the digits after the
rounded digit becoms zero.
For example, if you are rounding 452 to the nearest tens then the
number becomes 450.
Rule 2: If the digit you are rounding is followed by a 5, 6, 7, 8, or 9
then the digit you are rounding increases by one. All digits after the
rounded digit become zero.
For example, if you are rounding 452 to the nearest hundreds then the
number becomes 500.
So… Back to the Original Question
What if I have the number 245 200 000 and I
want it written with only 3 significant figures.
Which digit would I have to round?
If I wanted three sig. figs the number would be
written as
245 000 000
How could we put 245 200 000 into scientific
notation using only 3 sig. figs.
2.45 x 10 8
Another example:
Write 0.0003249914 into scientific
notation with only 4 sig figs.
This becomes
Now Try These:
Write each number 3 sig figs, then put the
number into scientific notation!
3456
2932
0.03499
0.05
WHY?
Scientists do a lot of measuring. When scientists use an
instrument (such as a ruler, graduated cylinder,
spectrophotometer or balance) to measure something,
it is important to take full advantage of the instrument.
However, they can’t cheat and record a better
measurement than the instrument is capable of. There
is an understanding among scientists of the proper way
to record valid measurements from any instrument.
When you are the scientist, you must record data in this
way. When you are reading other scientists’ work, you
must assume they recorded their data in this way.
Example: In a lab we have to measure the length of this Mg
strip. Using the ruler, how long do you think this piece of
Mg is?
Are we certain of these values?
From the values listed on the board do you think that
there was any agreement between any of these values?
When a measurement is recorded properly,
all of the digits that are read directly
(certain) and one
estimated (uncertain) digit are called
significant digits. The number of allowable
significant digits is
determined by the marks or gradations of
the instrument. Sometimes a “0” is the
estimated digit and
must be recorded.
Make an estimation of the length of the Mg strip.
What number(s) are we certain of here?
What number(s) is uncertain?
THINK ABOUT IT
• When humans use measuring instruments,
variation is expected. Everyone will estimate
differently between marks on the instrument.
On the other hand, digits that are certain
(based on marks on the instrument) should
not vary from person to person.
Make an estimation of the length of the Mg
strip.
What number(s) are we certain of here?
What number(s) is uncertain?