Transcript File

Conversions
Unit 2 - Math
Units:
 In science EVERY number comes with a unit.
(If you asked for a hundred DOLLARS for your birthday
and only got 100 PENNIES you would be a little
disappointed. They aren’t the same thing!)
Measurements
 English System: RIDICULOUS!!
 Metric System: Based on the number ten so
easy to work with.
 Length = meter (m)
 Mass = kilogram (kg)
 Temperature = Kelvin (K)
 Volume = Liter (L)
Standard Units:
 Time = second (s)
Letter
Name Number of Zeroes
Big/Small
k
kilo
3
1000x bigger
M
mega
6
million x
The prefix tells you how
far to shift the decimal
forward or backward.
G
giga
9
billion x
T
tera
12
trillion x
Example:
c
centi
-2
100x smaller
m
milli
-3
1000 x

micro
-6
million x
n
nano
-9
billion x
Prefixes:
1 km = 1 (000) m
1 cm = (0.0)1 m
Scientific Notation
https://m.youtube.com/watch?v=AWof6knvQwE
Scientific Notation
 Long numbers can be written
in a simplified form.
 We can tell the viewer how
far to slide the decimal
forward or backward by
multiplying by powers of ten
Steps:
1. First locate the decimal.
1234567.89
2. Next move the decimal until there is only ONE number in front of
it. (This number can NOT be a zero.)
1.23456789
3. Count the number of spaces you moved the decimal. This is the
number that goes with the 10. If the original number is BIG , the
exponent will be positive. If the original number is SMALL the
exponent will be negative.
We moved the decimal 6 places and the original number is BIG so the
exponent will be positive 6.
Steps (Cont.):
4. Keep only the first three numbers that you see. We
call the number of digits that we keep “significant figures”.
In this class we are going to always use three. Round the
last digit as needed. These three numbers go in front of
the 10.
1.23 456789
5. Write the final number. The official form looks like
1.23 x 106
…However, the short cut used by your calculator and the
homework grading system is to replace the ten with the
letter E.
Hiding Decimals:
 What if we have a number like 123,456,789?
 Where is the decimal?
…it is hiding at the far RIGHT side. In this case, it is after
the number 9.
 We move the decimal over 8 spaces.
 Note: 4 is less than 5 so we don’t round up and the
number becomes:
1.23 x 108
 On the homework enter it in like 1.23E8
Small Number Example:
 Let’s say that the answer to a homework
question was 0.000002467.
 This number is a pain to write by hand, so
let’s use scientific notation.
Steps:
 First: find the decimal near the beginning and move it
backward until there is only one number in front of it.
Remember that ZERO DOES NOT COUNT.
0.000002467
0000002.467
 Count the number of spaces the decimal moved
backward.
It moved 6 spaces
Steps (Cont.):
 The original number was very, very small. This means
that the six will be negative. Our final answer will have
a 10 -6 at the end.
 We only keep the first three numbers. Again, ZERO
DOES NOT COUNT. We must also look at the fourth
number to decide if we need to round.
0000002.467
Because 7 is bigger
than 5 we must round
the 6 to a 7.
2.47
Final Step:
 Putting everything together we get
2.47 x 10-6
 Enter this in the computer as 2.47E-6
 1234567.89=
1.23 x 106
(We keep three digits.)
 5.62 x 10 5 =
= 1.23E6
562,000
 Put 715 in your calculator = 4.75E12
(Don’t
forget to notice the E! It matters a LOT.)
 0.0000342619
=
3.43 x 10 -5
= 3.43E-5
(Negative power. Round if needed.)
 6.78 x 10 -3 =
0.00678
Scientific Notation:
 Examples: (Write these examples in your notes)
When Rounding:
 Do NOT round any of your answers until
the very, very end of the problem.
Otherwise the computer may mark you
wrong.
 Learn how to store numbers to the
memory of your calculator or else get in
the habit of writing them down completely
so that you don’t have problems with this.
Scientific Notation
Scientific Notation Challenge
The Number 0ne:
To change the units on a measurement without changing
the measurement itself you must multiply by the
number…
…One
The Number 0ne:
Let’s say you found a dress from a Paris magazine
that you loved.
You knew your
measurements in
inches but their size
chart was in
centimeters.
Would you want to change the value on your
measurements?
The Number 0ne:
NO!!!
If you changed the value on your measurements
they would not be the same measurements
anymore and the dress would not fit you….
But what if you kept the same measurements but
changed the the units? Then would the dress still
fit?
The Number 0ne:
Yes!!!
How can we do this?
By multiplying by the number 1.
The Number 0ne:
Any time you multiply by the number 1 what do you get?
The SAME thing you started with.
18 x 1 =
5
18
x1= 5
x1=
same x 1 = same
The Number 0ne:
This is why conversions work.
If we multiply your dress measurements by 1…
…then you will get the same measurements in different
units, giving you the same fitting dress in the end.
x1=
The Number 0ne:
Let’s say you are 5 feet 4 inches. Which doing the math
means you are 64 inches tall but you need your
measurement in cm for your perfect dress.
Doing the math we get…
64 in x 2.45 cm
= 156.8 cm
1 in
Wait!
Is 156.8 cm the same as 64 in?
The Number 0ne:
Yes!!!
Because all we have done is multiplied by the number
one which gets us the same thing we started with.
But how is
2.54 cm
=1
1 in
Because 1 in = 2.54 cm it simplifies down to 1.
1 in is the same thing as 2.54 cm…
The Number 0ne:
What if we had:
5
=1
2
=1
2
5
same
same
x
=1
x
apples
apples
=1
=1
The Number 0ne:
But what if I had:
7 days
=1
1 week
Does this equal one?
YES!!!
Why does this equal one?
Well is 7 days the same thing as 1 week?
YES!!!
The Number 0ne:
And any time I have
same
=1
same
The Number 0ne:
7 days
1 week
Comes from the conversion factor:
1 week = 7 days
We can write it like
7 days
1 week
or
1 week
7 days
The Number 0ne:
We will use similar conversion factors to multiply the value
we already have, by the number 1, to get our value into
the units we are looking for.
1 in = 2.54 cm
is one of these conversions and can be written like
1 in
2.54 cm
or
2.54 cm
1 in
The Number 0ne:
We basically can flip the fraction to what we
want so that we can cancel out the units we
don’t want anymore.
1 in
2.54 cm
or
2.54 cm
1 in
The Number 0ne:
What if we have to use a couple different conversions to
get us to the unit we want?
Is this ok?
Well does
still equal
x1 x1
x1 x1
=
?
YES!!!
The Number One:
We will use all of this information to make
conversions, to change from one unit to
another.
As we do what is called…
Dimensional Analysis…
Dimensional Analysis
(Train Tracks)
 STRATEGY: If you have a unit you don’t
want to have then. . . .
… Run it over!
A few things to remember…
 Units can be treated as mathematical variables.
 They can be multiplied, added, subtracted, or
divided.
 All the regular rules of algebra apply to them.
Basic Conversion:
 How many seconds are in a week?
1 Week
7 Days
1 Week
24 Hours
1
Days
60 Min
1 Hours
60 Seconds
1 Min
604,800 Seconds
If you walk one million inches, how
many miles is that?
Two Layer Conversion:
 My corn grows 5 in / week.
 How many feet / year is that?
5 in
1
ft
wk
12 in
1
wk
365 days
7
days
1 yrs
21.7
ft
yr
My dog can run 13 ft/s. How many
miles /hour is that?
Metric Conversions:
 The PREFIX is the first letter (it adjusts the size).
 The BASE unit is the second letter (it names the
unit).
Always Remember
1. Prefix gets a 1.
2. Base unit gets 10 to an exponent from the card.
3. Always convert to base unit fist.
Basic Conversion:
 How many millimeters are in 3.75 meters?
3.75 m
1 mm
10-3 m
3750
mm
How many Joules are in 5.6 kiloJoules?
Multiple step Conversion:
 How many kilobytes are in 4.5 gigabytes?
4.50 x 106
4.5 Gb
109 b
1 Gb
1 Kb
103 b
4,500,000 Kb
Convert 3.085 milliLiters to deciLiters.
(d = deci =/-1)
Combined Conversion:
 If I am 1.77 meters tall, how many feet is that?
1.77 m
1 cm
1 in
1 ft
10-2 m
2.54 cm
12 in
5.81
ft
How many minutes are in two million
s?