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There are many different units¬ in the English Standard System of Measurement.¬

Converting between units¬ can be tricky because it requires you to memorize¬ many arbitrary conversion factors.¬

Because partial units are denoted using fractions¬, adding and subtracting them is more difficult.¬

Some people like¬ the fact that you don’t have to deal with lots of zeros.

The metric system avoids them¬ by using prefixes.

The metric system doesn’t¬ use arbitrary conversion factors or fractions,¬ just decimals¬ and powers of 10.

The names of the units¬ are short¬ and have simple letter symbols.

And the metric system¬ is also the world standard.

In fact,¬ it’s used to define the English Standard System.¬

Meters,¬ denoted by a lower case m, are the unit of length. One meter is a few inches longer than a yard.

Liters,¬ represented by either an upper or lower case L, are the unit of volume. One liter is a little over a quart.

Grams,¬ represented by a lower case g, are the unit of mass. One gram is a little over one thirtieth of an ounce – a pretty small quantity.

Each prefix has a name.¬ Giga, Mega, Kilo, Deci, etc.

Each has a representative symbol,¬ For example, capital M for mega and lower case k for kilo.

Note that the prefix micro is represented by the Greek letter mu (which looks like a “u” with a funny line in front of it).

And each prefix has a magnitude¬ represented by a power of ten. For example, Giga means a magnitude of 10 to the ninth, or billions.

Whereas deci means a magnitude of 10 to the minus one, or tenths.

Besides the base units of meters, liters, and grams,¬ these prefixes are also commonly used with two other units that are not specific to the metric system, namely seconds and bytes.¬

A number¬ represents the quantity.

Letters¬ are used for the magnitude, if present, and the basic unit.

So, for example, one gram¬ is abbreviated as the number one followed by the letter gee.

Two meters¬ is represented by a two and an em.

Twelve milligrams¬ is abbreviated by twelve-em-gee and ten kilometers¬ is represented by ten-kay-em.¬

What unit could we use to measure¬ the volume of a swimming pool?

This volume is probably best represented by¬ kiloliters or megaliters.

What unit could we use to measure¬ the mass of a car?

This mass is probably best represented by¬ megagrams or gigagrams.

What unit should we use to measure¬ the length of a pencil?

Pencil length is probably best represented by¬ centimeters.

What unit could we use to measure¬ the height of tree?

The height of a tree is probably best represented by¬ meters.

And what unit could we use to measure¬ the volume of a shoebox?

This volume is probably best represented by¬ liters

Notice that if there is no prefix, the symbol for liter is a capital L.¬

And yes, I know we have the inch markers¬ upside down on the bottom. That’s okay because we’re not going to use them.

Notice the little¬ MM and CM, they stand for millimeters and centimeters.

The longer lines to the right the numbers denote centimeters and the intervening hash marks, millimeters.

So¬ how wide is the dime? Let me make this a little easier on you by adding¬ some lines.

Got it? Okay, the dime is¬ 18 millimeters or 1,8 centimeters wide.¬

For example¬, we can add a prefix to 3100 meters and change it to 3.1 kilometers.

Or we can change¬ prefixes and quantities to go from zero-point-two microseconds to two-hundred nanoseconds.

An easy way¬ to do these conversions is to use the metric conversion ruler.¬

Notice that the top row consists of magnitudes represented by the powers of ten.

We put each prefix (and its abbreviation) under the appropriate magnitude.

Under ten-to-the-zero, which is, after all, just one, we put the base units.¬

Let’s try to change¬ five-point-three megameters to kilometers.

First we look at the metric conversion ruler¬ to find where the prefixes¬ fall on the line.

Then we count¬ the number of spaces between the prefix lines.¬ In this case there are three spaces between mega and kilo.

We note the direction¬ we go from one prefix to the other.¬ The direction from mega to kilo is to the right.

So, to convert 5.3 megameters to kilometers¬ we move the decimal point three places to the right.

This means that¬ five-point-three megameters is equal to fifty-three-hundred kilometers

since fifty-three-hundred is what you get when you move the decimal point in five-point-three three places to the right.¬

We see that¬ the number of spaces between the prefixes is once again¬ three.

This time¬ going from milli to grams means a move to the left.

So that means that to do the conversion¬ we move the decimal point three places to the left.

Therefore,¬ one-thousand-twenty-four milligrams is equal to one-point-zero-two-four grams¬

Seven-point-one-one micrograms is equal to how many nanograms?

To go from¬ micro to nano we move¬ three places to the right.

Moving the decimal point three places gives us¬ seven-thousand-one-hundred-ten nanograms.

Zero-point-two-nine-three-four¬ kilograms equals how many decigrams?

The distance from¬ kilo to deci is four places and the direction¬ is to the right.

Moving the decimal point we get¬ two-thousand-nine-hundred-thirty-four decigrams.

Twenty-one-point-six-six-five¬ centiliters is how man milliliters?

Milli ¬ is only one space away from centi and the direction is again¬ to the right.

Therefore, the answer is¬ two-hundred-sixteen-point-six-five milliliters.

Finally,¬ seven-hundred-three-point-nine-four micrometers is how many millimeters?

The distance between prefixes¬ is three places and the direction is¬ to the left.

So, this results in¬ an answer of Zero-point-seven-zero-three-nine-four millimeters.¬

- 1. V1.3 20080829 1 The Metric System Workshop This short presentation will go over the units used in the metric system, their naming conventions, and how to convert between different metric units.
- 2. V1.3 20080829 2 What Americans Are Used To The English Standard System Inches and gallons and pounds (oh my!) Many different units Inches, feet, yards, miles, … Ounces, cups, pints, quarts, gallons, … Many conversion factors 12 inches in a foot 5280 feet in a mile 16 ounces in a pound Fractional units ¼ inch, ½ gallon, ¾ pound, …
- 3. V1.3 20080829 3 Why People Like the Metric System No piles of zeros Just prefixes No arbitrary conversion factors or fractions Only decimals Easy to pronounce and write Short names and simple letter symbols World standard It’s used to define the English Standard System!
- 4. V1.3 20080829 4 What’s the metric system all about?
- 5. V1.3 20080829 5 It’s All About Three Basic Units Meters Length, e.g., your height Represented by the letter m One meter is a few inches longer than a yard Liters Volume, e.g., the size of a car’s gas tank Represented by the letter l or L One liter is a little more than a quart Grams Mass, e.g., the mass of a penny Represented by the letter g One gram is a little over one thirtieth of an ounce
- 6. V1.3 20080829 6 And It’s All About Prefixes NAME Giga Mega Kilo Deci Centi Milli Micro Nano Magnitude 109 106 103 10-1 10-2 10-3 10-6 10-9 Symbol G M k d c m µ n (Besides meters, liters, and grams, the prefixes are also used for other units – seconds and bytes – that are not metric system specific)
- 7. V1.3 20080829 7 Putting Units and Prefixes Together Metric measurements consist of A quantity, e.g., two or 101 An optional prefix for the magnitude of the quantity , e.g., kilo or mega And one of the three basic units. For example Thirty liters Two kilometers Six decigrams
- 8. V1.3 20080829 8 Abbreviating Measurements Numbers and symbols are used to abbreviate measurements The number represents the quantity Symbols represent the magnitude and unit One gram is abbreviated as 1 g Two meters is represented by 2 m Twelve milligrams is abbreviated as 12 mg Ten kilometers is represented by 10 km
- 9. V1.3 20080829 9 What Units Would You Use? The volume of a swimming pool kiloliters (kl) or megaliters (Ml) The mass of a car megagrams (Mg) or gigagrams (Gg) The length of a pencil centimeters (cm) The height of tree meters (m) The volume of a shoebox liters (L)
- 10. V1.3 20080829 10 Down here are the inches. Yes, I know they’re upside down. The little MM and CM stand for millimeters and centimeters So, how wide is the dime? The End of a Ruler 18 mm or 1.8 cm
- 11. V1.3 20080829 11 Converting Between Prefixes Sometimes we want to change from one prefix to another For example, changing 3100 meters to 3.1 kilometers Or 0.2 microseconds to 200 nanoseconds To do this we use the metric conversion ruler
- 12. V1.3 20080829 12 109 108 107 106 105 104 103 102 101 10-1 100 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 giga- (G) mega- (M) kilo- (k) deci- (d) centi- (c) milli- (m) micro- (µ) nano- (n) Base unit (g, m, L, sec, or byte) Metric Conversion Ruler
- 13. V1.3 20080829 13 Using the Metric Conversion Ruler Change 5.3 megameters to kilometers Look at where the prefixes fall on the line Count the number of spaces between them Look at the direction between prefixes Move the decimal point 3 places to the right 5.3 Mm = 5300 km 107 106 105 104 103 102 mega- kilo- to the right ←3 spaces→
- 14. V1.3 20080829 14 Another Conversion Example Change 1024 milligrams to grams Move the decimal point 3 places to the left 1024 mg = 1.024 g 101 100 10-1 10-2 10-3 10-4 gram milli- 3 spaces to the left
- 15. V1.3 20080829 15 Conversion Examples 7.11 µg = ? ng 7110 ng 0.2934 kg = ? dg 2934 dg 21.665 cl = ? ml 216.65 ml 703.94 μm = ? mm 0.70394 mm 4 spaces to the right 103 102 101 10-1 kilo- deci- 100 10-2 centi- 10-3 milli- 1 space to the right 10-3 10-4 10-5 10-6 milli- micro-3 spaces to the left 3 spaces to the right 10-6 10-7 10-8 10-9 micro- nano- 10-9
- 16. V1.3 20080829 16 The End Please download some conversion worksheets to elp hone your skills http://sciencespot.net/Media/metriccnvsn2.pdf

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