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**METRIC MEASUREMENT UNITS**

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**METRIC UNITS OF LINEAR MEASURE**

Based on powers of 10 Most frequently used units of length: kilometer meter centimeter millimeter

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METRIC LINEAR UNITS The following list shows several units of linear measure and their lengths in meters: 1 kilometer (km) = meters (m) 1 hectometer (hm) = meters (m) 1 dekameter (dam) = meters (m) 1 meter (m) = meter (m) 1 decimeter (dm) = meter (m) 1 centimeter (cm) = meter (m) 1 millimeter (mm) = meter (m) There are a lot of these conversions on your conversion sheet with the back covering the prefixes and some of the conversions covered on the front. In metric, the unit is not as important as the prefix.

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**CONVERTING METRIC LENGTHS**

Express 75 decimeters as meters Express 1.95 centimeters as millimeters **Notice I converted to meters and back to millimeters. This is not required, you can slide the decimals but most non-metric using people have trouble sliding the decimal. Especially when we get to other dimensions. The conversions used above are on your conversion sheet and keep you from sliding the wrong direction.

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**METRIC AREA CONVERSIONS**

Express 84.5 square centimeters as square decimeters These conversions are not all on your sheet but to go from first to second dimension you are squaring measurements from the first….so 10dm in a meter in linear (first) so 100dm2 = 1m2 Express 5.6 square hectometers as square Dekameters Capital D to show Deka instead of deci Dam is also used for Dekameters

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METRIC VOLUME UNITS Express 38,500 cubic millimeters as cubic decimeters Convert 2.5 km3 as cm3 (also called cc)

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**METRIC UNITS Commonly used capacity-cubic measure equivalents:**

1 milliliter (mL) = 1cubic centimeter (cm3) 1 liter (L) = 1cubic decimeter (cm3) 1 liter (L) = cubic centimeters (cm3) 1000 liters (L) = 1 cubic meter (m3) Commonly used weight (mass) measure equivalents: 1000 milligrams (mg) = 1gram (g) 1000 grams (g) = 1kilogram (kg) 1000 kilograms (kg) = 1 metric ton (t)

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**COMPOUND UNITS Kilometers per hour can be written:**

Products or quotients of two different units Converted to smaller or larger equivalent compound unit measures using unity fractions Expressed using per such as kilometers per hour which indicates division Kilometers per hour can be written:

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**COMPOUND UNIT EQUIVALENTS**

Simple needs only one unit to be converted Complex needs more than one unit to be converted Express kilometers per hour as meters per minute

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**Extremely large and small measures**

Top and bottom of chart on conversion sheet Tera, Giga, Mega are very large (heard in computer world and astrology) micro, nano, pico are very small (heard in biology) They work the same in unity fraction method just more conversions. With these you will use scientific notation in most cases. It is 2.4x1020 m to the sun. How far is that in Terameters? A cell is 5.7 micrometers thick. How many picometers is that?

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**METRIC-CUSTOMARY CONVERSIONS**

Length 1 in = cm 1 ft = cm 1 yd = m 1 mi = km Weight 1 oz = g 1 lb = kg 1 (short) ton = kg Volume 1 cu in. (in3) = cm3 1 fl oz = cm3 1 tsp = mL 1 tbsp = mL 1 qt = L 1 gal = L

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**EXAMPLES Convert 8.24 in to millimeters**

Convert 9.25 ft2 to square centimeters

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**PRACTICE PROBLEMS Express 63 meters as centimeters**

Express 4.75 Dekameters as kilometers Express hectometers as millimeters Express 49.3 decimeters as Dekameters Express square decimeters as square centimeters Express 1.09 square Dekameters as square hectometers Express 2.5 cubic feet as cubic meters

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**PRACTICE PROBLEMS (Cont)**

Express 123,500 cubic inches as cubic centimeters Express 1,260 cm3 as dm3 Express cubic meters as cubic centimeters Express 13.5 liters as gallons Express 4.6 cubic meters as cubic inches Express 18.2 ft/min as km/hr Express 1.2 short tons/cubic foot as pounds/cubic inch

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**PRACTICE PROBLEMS (Cont)**

A bullet travels at 1500 miles per hour. How many meters per second is that? You receive measurements that specify a 2.5 square meter area for a new machine. How many square inches do you need to clear out? A map in Canada says it is 350 kilometers to the next city. How many miles is the trip? A cell has a thickness of 3.2 nanometers. In scientific notation, how many meters is that? If a circuit needs 0.5 Megawatts, how many deciwatts are needed? If I have a tank that holds 350 gallons, how many milliliters does it hold?

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**PROBLEM ANSWER KEY 6300 cm 0.0475 km 760 mm 0.493 dam 8.4 cm2**

hm2 m3 2.024 m3 1.26 dm3 cm3 3.57 gal cu in 19.97 km/hr 1.389 lb/ cu in 670.57m/sec in2 mi 3.2x10-9 m 5.0x106 dw mL

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Welcome to Survey of Mathematics

Welcome to Survey of Mathematics

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