1. Conversions
Unit 2 - Math

2. 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!)

3. Measurements English System: RIDICULOUS!!
Metric System: Based on the number ten so easy to work with.
The English System of measurement (inches, feet, yards, etc) is absolutely ridiculous! Nobody uses it anymore except for America! (Not even England uses it!) The units are based on silly things and the conversion factors are random and must be memorized. For example, a “foot” is the length of the King of England’s foot. There are 12 inches in a foot. Why the magic number 12? Just because.
The Metric System (also known as SI units) is a MUCH more friendly system for measuring things. It is based around the number 10 (just like our counting system) which makes unit conversions incredibly easy. You just end up moving the decimal.

4. Standard Units: Time = second (s) Length = meter (m)
Mass = kilogram (kg)
Temperature = Kelvin (K)
Volume = Liter (L)
Different measurements are required for different data. For example, you don’t measure length in seconds or weight in meters. Standard units have been selected to measure different types of data. Unless told otherwise, all homework solutions should be given in Standard Units. All other units in this class are obtained by combining these units in different ways.

5. The prefix tells you how far to shift the decimal forward or backward.
Letter k M G T c m  n
Name
Number of Zeroes
Big/Small
Prefixes:
kilo 3
1000x bigger
mega 6
million x
The prefix tells you how far to shift the decimal forward or backward.
Example:
1 km = 1 (000) m
1 cm = (0.0)1 m
giga 9
billion x
tera 12
trillion x
centi -2
100x smaller
milli -3
1000 x
micro -6
million x
nano -9
billion x

6. https://m.youtube.com/watch?v=AWof6knvQwE
Scientific Notation

7. 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
Scientific Notation

8. Steps:
1. First locate the decimal Next move the decimal until there is only ONE number in front of it. (This number can NOT be a zero.) 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.

9. 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
5. Write the final number. The official form looks like x 106
…However, the short cut used by your calculator and the homework grading system is to replace the ten with the letter E.
456789

10. 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

11. Small Number Example:
Let’s say that the answer to a homework question was
This number is a pain to write by hand, so let’s use scientific notation.

12. 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.
Count the number of spaces the decimal moved backward.
It moved 6 spaces

13. Steps (Cont.):
The original number was very, very small. This means that the six will be negative. Our final answer will have a 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.
2.47
Because 7 is bigger than 5 we must round the 6 to a 7.

14. Final Step: Putting everything together we get 2.47 x 10-6
Enter this in the computer as 2.47E-6

15. Scientific Notation: Examples: (Write these examples in your notes)
= x 106 = 1.23E6 (We keep three digits.)
5.62 x = 562,000
Put 715 in your calculator = 4.75E12 (Don’t forget to notice the E! It matters a LOT.)
= 3.43 x = 3.43E-5 (Negative power. Round if needed.)
6.78 x =
Scientific Notation:

16. 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.
When Rounding:

17. Scientific Notation Challenge

18. The Number 0ne:
To change the units on a measurement without changing the measurement itself you must multiply by the number…
…One

19. The Number 0ne:
Let’s say you found a dress from a Paris magazine that you loved. Would you want to change the value on your measurements?
You knew your measurements in inches but their size chart was in centimeters.

20. 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?

21. Yes!!! The Number 0ne: By multiplying by the number 1.
How can we do this?
By multiplying by the number 1.

22. The SAME thing you started with.
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
x 1 = 18
same
x 1
= same
x 1 = 5

23. 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. x 1 =

24. 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 Wait! Is cm the same as 64 in?
2.45 cm
= cm
1 in

25. 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 in Because 1 in = 2.54 cm it simplifies down to 1. 1 in is the same thing as 2.54 cm…
= 1

26. The Number 0ne: What if we had: 5 x 2 = 1 = 1 2 same = 1 same apples

27. The Number 0ne:
But what if I had: 7 days 1 week Does this equal one? Why does this equal one? Well is 7 days the same thing as 1 week?
= 1
YES!!!
YES!!!

28. The Number 0ne: 1
And any time I have same 1 1
= 1 1 1 1 1

29. 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

30. 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

31. 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

32. 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 x 1
still equal
x 1
x 1
x 1 = ?
YES!!!

33. 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…

34. Dimensional Analysis (Train Tracks)
STRATEGY: If you have a unit you don’t want to have then
… Run it over!

35. 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.

36. Basic Conversion: How many seconds are in a week? 1 Week 7 Days 24
Hours 60
Min 60
Seconds
604,800
Seconds 1
Week 1
Days 1
Hours 1
Min

37. If you walk one million inches, how many miles is that?

38. Two Layer Conversion: My corn grows 5 in / week.
How many feet / year is that?
5 in 1 ft 1 wk
365
days
21.7 ft wk 12 in 7
days 1
yrs yr

39. My dog can run 13 ft/s. How many miles /hour is that?

40. Metric Conversions:
The PREFIX is the first letter (it adjusts the size).
The BASE unit is the second letter (it names the unit).

41. Always Remember Prefix gets a 1.
Base unit gets 10 to an exponent from the card.
Always convert to base unit fist.

42. Basic Conversion: How many millimeters are in 3.75 meters? 3.75 m 1 mm
3750 mm
10-3 m

43. How many Joules are in 5.6 kiloJoules?

44. Multiple step Conversion:
How many kilobytes are in 4.5 gigabytes?
4.50 x 106
4.5 Gb
109 b 1 Kb
4,500,000 Kb 1 Gb
103 b

45. Convert 3.085 milliLiters to deciLiters. (d = deci =/-1)

46. Combined Conversion: If I am 1.77 meters tall, how many feet is that?cm 1 in 1 ft
5.81 ft
10-2 m
2.54 cm 12 in

47. How many minutes are in two million s?