Understanding Metric Prefixes

1
Understanding Metric Prefixes

• The following metric prefixes can be used in
  front of any one of the base units to change the
  value by a power of ten. Since all of the units
  change by powers of ten, converting between the
  different units is as simple as moving the
  decimal place.

2
Understanding Metric Measurements (cont.)

• The following is a list of some of the most
  common large metric prefixes and their meanings
• Tera- 1,000,000,000,000 (1012)
• Giga- 1,000,000,000 (109)
• Mega- 1,000,000 (106)
• Kilo- 1,000 (103)
• Hecto- 100 (102)
• Deka- 10 (101)

3
Understanding Metric Measurements (cont.)

• The following is a list of some of the most
  common small metric prefixes and their meanings
• Deci- 1/10 (10-1)
• Centi- 1/100 (10-2)
• Milli- 1/1000 (10-3)
• Micro- 1/1,000,000 (10-6)
• Nano- 1/1,000,000,000 (10-9)
• Pico- 1/1,000,000,000,000 (10-12)
• Femto- 1/1,000,000,000,000,000 (10-15)

4
Putting it all into perspective

• The relationship between these units can be
  understood by putting them all on a place value
  line.
• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• While it is possible to convert between metric
  units by using dimensional analysis, most people
  find it easier to simply move the decimal to the
  left or the right, as required, to determine the
  value of the new unit.
• The question is.how do we know whether to move
  the decimal to the left or to the right.and how
  many places?

5
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Step 1 Write the above chart at the top of your
  paper from memory!
• What???!!! (You must be joking!)
• No.really.
• I cant do that!
• Yes, you can. ?
• By using mnemonics.thats the word that means
  memory aid. ?

6
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• So lets talk about that mnemonic thing.
• How am I supposed to remember this?
• The trick is to make it easy for yourself. Im
  going to help you with this one, but I want you
  to be able to come up with your own way to
  remember other bits of information as we go
  through the course. ? I wont always be there to
  help you.

7
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Do you remember how you learned the order of the
  planets?
• My very educated mother just served us nine
  pizzas. (Since we lost Pluto, now its just
  nachos. ? )

• H.O.M.E.S. is an acronym to help us remember the
  names of the Great Lakes Can you name them?
• Huron, Ontario, Michigan, Erie, Superior

• SO.this mnemonic thing might be a sentence, if
  order is important, or it might be an acronym if
  order is NOT important.

8
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Is order important here?
• Yes.it is.
• Do you remember the Kangaroos hop down mountains
  drinking chocolate milk sentence that you used
  when you were only working with a few of these
  metric prefixes?
• Were going to expand upon that just a little
  bit.
• How about this one?......
• Ten Gorgeous Mexican Kids Hop Down Mountains
  Drinking Chocolate Milk Making Nana Pretty
  Furious! (Sort of catchy, huh?)

9
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Ten Gorgeous Mexican Kids Hop Down Mountains
  Drinking Chocolate Milk Making Nana Pretty
  Furious!
• The first letter of each word corresponds to the
  first letter of each metric prefix.
• If you can remember the sentence, you can
  remember the first letter of each word.
• If you can remember the first letter of each
  word, you can write the words. ?

10
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets repeat the sentence together.
• Ten Gorgeous Mexican Kids Hop Down Mountains
  Drinking Chocolate Milk Making Nana Pretty
  Furious!
• Lets say it again.
• Now lets say the names of the prefixesout
  loudtogether.

11
Mini-assessment

• Okay.take out a clean sheet of paper. Think
  about the sentence, but dont say it out loud.
• Turn your notebook paper sideways, and write the
  first letter of each word of the sentence.
• Now, try to write the name of the metric prefix
  which corresponds to each letter.
• Well take five minutes. Bring me your paper when
  you finish.
• www.onlinestopwatch.com

12
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Okay.so weve got the words down. Now for the
  numbers.
• First, lets realize that the base unit is the
  starting point. As in graphing, the starting
  point is always zero.
• As we move to the left or to the right, our
  exponents change, first in increments of 1,
  then after we reach 3, in increments of 3.
• 1,2,3,6,9,12 or -1,-2,-3,-6,-9,-12,-15.
• Remember that 0 is in the middle.

13
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• So.lets try it together. The middle is 0.
  Then
• To the left, we have
• 1,2,3,6,9,12
• Or to the right we have
• -1,-2,-3,-6,-9,-12,-15.
• REMEMBER that the numbers after the base unit
  represent decimal numbers and have negative
  exponents.

14
Mini-assessment

• Using the same piece of paper you already used on
  the last activity, turn the paper over and lets
  see what we know.
• First, think about our sentence.
• Then, write the first letter of each wordacross
  your page (turned sideways) from left to right.
• For each letter, write the corresponding metric
  prefix.
• Finally, write the power of ten which represents
  each of the prefixes.

15
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Okay, now that we can write our chart, lets
  figure out how to use it to convert between
  metric measures.
• Lets say that I want to change 76 mm to _______
  cm.
• To move from mm to cm on the chart, you move to
  the left.
• Therefore, the decimal will move left, too.

• But how do you know how many places to move it?

16
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• To change 76 mm to cm, take the positive
  difference between their exponentsin this
  case(-3) (-2) (-1). Positive difference of
  1.
• Thats how many places youll move the decimal1.
• And since you move to the left to get from mm to
  cm on the chart, youll move your decimal to the
  left.1 place.
• ? 1 place
• Since there is no decimal in 76 mm, it is
  understood to come at the end of the number.
• 76. mm 7.6 cm

17
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets change 3.65 Tm to _______km
• What direction do we move to get from Tm to km?
• What is the positive difference between their
  exponents?

18
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets change 3.65 Tm to _______km
• What direction do we move to get from Tm to km?
• To the right
• What is the positive difference between their
  exponents?
• 12 3 9
• That means we move the decimal 9 places to the
  right.
• 3.65_ _ _ _ _ _ _ The decimal will now be at
  the end, and all of the blanks will become 0.
  No need to write the decimal.
• 3.65 Tm 3 650 000 000 km

19
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets change 4.67 mm to _______dam
• mm means micrometers
• dam means dekameter
• What direction do we move to get from mm to dam?
• What is the positive difference between their
  exponents?

20
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets change 4.67 mm to _______dam
• What direction do we move to get from mm to dam?
• To the left
• What is the positive difference between their
  exponents?
• (-6) (1) (-7), so the positive difference is
  7.
• That means we move the decimal 7 places to the
  left.
• _ _ _ _ _ _4.67 The decimal will now be seven
  places to the left of its original position as
  indicated by the caret.
• 4.67 mm 0.000000467 dam

21
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets change 0.35 cm to _______mm
• What direction do we move to get from cm to mm?
• What is the positive difference between their
  exponents?

22
This is how we do it.

• tera- giga- mega- kilo- hecto- deka-
  METRIC deci- centi- milli- micro- nano-
  pico- femto-
• 1012 109 106 103 102
  101 BASE 10-1 10-2
  10-3 10-6 10-9 10-12
  10-15
• UNIT
• 100

• Lets change 0.35 cm to _______mm
• What direction do we move to get from cm to mm?
• To the right
• What is the positive difference between their
  exponents?
• (-2) (-6) (4), so the positive difference is
  4.
• That means we move the decimal 4 places to the
  right.
• 0.35_ _ The decimal will now be four places
  to the right of its original position as
  indicated by the caret.
• 0.35 cm _3500_mm (no need to write the 0 in
  the front)