1. Conversion of units

2. Metric conversion
Unlike English units like the pound, ounce, foot, yard… metric units are related by multiples of 10
There are 10 mm in every cm
There are 100 cm (10*10) in every m
There are 1000 m (10*10*10) in every km

3. Metric Symbols Used as prefixes before units Ex: Km = kilometer
Cg = centigram
Ghz = Gigahertz
Pm = picometer

5. How to convert using the chart

6. Convert on scale
Giga 100, 10, Mega 100, 10, Kilo Hecto Deka Base deci centi milli 1/ / micro 1/ / Nano
000, 000, meter , , ,
gram , ,
second
Determine direction: Put your finger on original prefix. Does your finger move left or right to reach the final prefix?
The direction your finger travels is the direction the decimal moves.
Move the decimal once for each step moved
If you run out of numbers, fill in with zeros.

8. Conversion to smaller units
If you are converting to a smaller unit (going down the steps) , multiply the unit by the number of 10’s equal to # of steps.
This is same as moving the decimal to the RIGHT as the number of steps

9. Example
16.0 m = _____ mm
You walk down 3 stairs from meters level to millimeters level
Walking down means you multiply 16.0 by 3 10’s OR move the decimal place to the right 3 spaces
Either way the correct answer is 16,000 mm

10. In comp book Practice questions: How many cm equal 15.7 km?
How many ms (milliseconds) equal 45.3 Ds (Dekaseconds)?

11. Answers
1,570,000 cm
453,000 ms
Notice that converting to smaller units result in larger values
It takes more of the tinier unit to equal a single big unit (ex. 100 cm needed to = 1 m)

12. Other examples

13. Convert to larger units
If you are converting to a larger unit, divide the unit by the number of 10’s equal to number of steps
This is the same as moving to the LEFT the number of spaces equal to the number of steps

14. Example Determine the number of km that equal 1340 m
You move up 3 steps from meter level to kilometer level
This requires you to divide 3 10’s in the value or move the decimal 3 spaces to the left
Either way the correct answer is 1.34 km

15. Try these in your comp book
Convert 298,000 mm to an equal number of Hm (hectometers).
Convert 456 g (grams) to and equal number of kg (kilograms)

16. Answers Answer = 2.98 hm Answer is 0.456 kg
Notice that the final numbers are smaller than the originals.
Notice also that the units (grams, seconds, meters) were all dealt with the same way

17. Conversion Factors we use most often :
1 meter = 100 centimeters
1 meter = 1000 millimeters
1 kilometer = 1000 meters
Could interchange seconds, grams, Newtons, Joules for meter

18. Shortcut Conversion for velocity
Divide your velocity in (km/hr) by 3.6 to get the velocity in (m/s) OR
To convert from m/s to km/h multiply by 3.6
To convert from km/h to m/s divide by 3.6

19. Time conversions 1 minute = 60 seconds 1 hour = 60 minutes
1 day = 24 hours
1 year = 365 days (approximation)

20. Dimensional analysis
A method to convert time or any other complex value with many units
All that is done is multiply value by 1 or more forms that have the value of one.

21. Forms of one Math wise: 1 = 2/2 =5/5 = 13/13 = 8.2 /8.2
If 1 minute = 60 seconds
then 1 min/60 s = 1 = 60 s / 1 min
Any fraction where the value of the top = the value of the bottom has an overall value of 1

22. Multiplying value by 1
Any value multiplied by 1 has the original value
But there is a way to change the units

23. An Example: Convert 645 seconds into the equivalent number of minutes
To do so…
Take 645 s and multiply by [ 1 min / 60 s]
645 s * 1 min /60 s
Second units cancel out, leaving minutes
(645*1)/60 = min

24. Try these in your comp book
47.5 minutes = _____ hr
8 days = ______ min

25. Answers
About 0.79 hr
11,520 min

26. Scientific notation

27. Scientific Notation A way to write very large or very small
Used to determine precision of value
A number between 1-10 x 10 to an exponent
Positive exponents for large #
Negative exponents for small #

29. To convert Small # to Sci Notation Large # to Sci Notation
To convert a small number to scientific notation, multiply the number by 10 as many times as is needed to get a digit value greater than 1 and less than 10. Multiply this digit value by an exponential term where the exponent is the negative number of times you have multiplied by 10.
To convert a large number to scientific notation, divide the number by 10 as many times as is needed to get a digit value less than 10 and greater than 1. Multiply this digit value by an exponential term where the exponent is the number of times that you have divided by 10.
= 1.23x10-8
= 1.23x109

30. Engineering button

31. Try
6,907,800,000
Answer
x109

32. Try
Answer:
8.007 x 10-8