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.

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 (10^12) Giga- 1,000,000,000(10^9) Mega- 1,000,000(10^6) Kilo- 1,000 (10^3) Hecto- 100 (10^2) Deka- 10 (10^1)

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)

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 BASE UNIT 10 0 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?

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Step 1: Write the above chart at the top of your paper… …from memory! What???!!! (You must be joking!) No….really. I can’t do that! Yes, you can. By using mnemonics….that’s the word that means memory aid.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 So let’s talk about that mnemonic thing. How am I supposed to remember this? The trick is to make it easy for yourself. I’m 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 won’t always be there to help you.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 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 it’s 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.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 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? We’re 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?)

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 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.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s repeat the sentence together. Ten Gorgeous Mexican Kids Hop Down Mountains Drinking Chocolate Milk Making Nana Pretty Furious! Let’s say it again. Now let’s say the names of the prefixes…out loud…together.

Mini-assessment Okay….take out a clean sheet of paper. Think about the sentence, but don’t 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. We’ll take five minutes. Bring me your paper when you finish.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Okay….so we’ve got the words down. Now for the numbers. First, let’s 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.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 So….let’s 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.

Mini-assessment Using the same piece of paper you already used on the last activity, turn the paper over and let’s see what we know. First, think about our sentence. Then, write the first letter of each word…across 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.

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Okay, now that we can write our chart, let’s figure out how to use it to convert between metric measures. Let’s 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?

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 To change 76 mm to cm, take the positive difference between their exponents…in this case…(-3) – (-2) = (-1). Positive difference of 1. That’s how many places you’ll move the decimal…1. And since you move to the left to get from mm to cm on the chart, you’ll 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

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s 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?

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s 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 Tm = km

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s change 4.67  m to _______dam  m – means micrometers dam means dekameter What direction do we move to get from  m to dam? What is the positive difference between their exponents?

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s change 4.67  m to _______dam What direction do we move to get from  m 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  m = dam

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s change 0.35 cm to _______  m What direction do we move to get from cm to  m? What is the positive difference between their exponents?

This is how we do it…. tera- giga- mega- kilo- hecto- deka- METRIC deci- centi- milli- micro- nano- pico- femto BASE UNIT 10 0 Let’s change 0.35 cm to _______  m What direction do we move to get from cm to  m? 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 cm = _3500_  m (no need to write the ‘0’ in the front)