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III. THE METRIC SYSTEM

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Recall… 2 parts A number and a unit Units = what was measured

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A. The Metric System Developed in France in 1795 Revised in 1960 Le Système International d’Unités The International System of Units or “SI Units”

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B. SI Base Units Length (distance) : Mass : Volume : Time : meter (m) gram (g) Liters (L) second (s)

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Practice What base unit would you choose to measure: 1. The length of a tree branch? 2.The volume of a soda bottle? 3. The mass of a chocolate bar? ~1.5 meters 2 liters ~450 grams

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C. Metric Prefixes PREFIX + BASE UNIT = a metric unit centi + meter = centimeter (cm) kilo + gram = kilogram (kg) milli + liter = milliliter (mL) Prefixes are based on powers of 10

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D. Exponent Review 10 x 10 = base x = exponent; tells how many times 10 is multiplied by itself 10 2 = 10 x 10 = 100 10 -x = 10 -2 = = = _1_ 10 x _1_ 10 2 _1_ 100 0.01

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D. Exponent Review Cont. If the exponent is POSITIVE, the number is larger than 1 10 3 is 1000 (1 with 3 zeroes) 10 5 is 100000 (1 with 5 zeroes) If the exponent is NEGATIVE, the number is less than 1 10 -3 is 0.001 (1 with 3 zeroes) 10 -5 is 0.00001 (1 with 5 zeroes)

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NameSymbol Numerical Value Power of Ten mega-M1,000,00010 6 kilo-k1,00010 3 hecto-h10010 2 deca-da1010 1 Base Units meters (m), liters (L), grams (g), seconds (s) 10 0 decid0.110 -1 centi-c0.0110 -2 milli-m0.00110 -3 micro- µ 0.00000110 -6 E. Metric Prefixes

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E. Metric Prefixes Cont. MEGA (M) King Henry Died By Drinking Chocolate Milk micro (µ) MEGA (M) kilo (k) hecto (h) deca (da) base unit deci (d) centi (c) milli (m) micro (µ)

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Practice What is the prefix? 1. µ 2. m 3. h 4. c 5. da 6. k 7. d 8. M

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F. Metric Conversions (Math/AP way) Step 1: Identify powers of 10 for each prefix Base unit with no prefix = 10 0 Step 2: subtract the exponents…move the decimal that many places A POSITIVE difference = move decimal to the right A NEGATIVE difference = move decimal to the left Example: 1.6 liters = _______ milliliters L: 10 0 mL: 10 -3 Subtract exponents: 0 – (-3) = +3 Move decimal 3 places to the right 1600

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F. Metric Conversions (Math/AP way) Step 1: Identify powers of 10 for each prefix Base unit with no prefix = 10 0 Step 2: subtract the exponents…move the decimal that many places A POSITIVE difference move decimal to the right A NEGATIVE difference move decimal to the left Example: 2.54 cm = _____________ kilometers (km) cm: 10 -2 km: 10 3 Subtract exponents: -2 – (3) = -5 Move decimal 5 places to the left 0.0000254

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Practice 1000 mg = _______ g 0.15 hm = _________ mm

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G. Metric Conversions (Easy Way) deci- (drinking) centi- (chocolate) milli- (milk) base unit (by) kilo- (king) hecto- (henry) deca- (died) Example: 36 kg = ______ cg

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G. Metric Conversions (Easy Way) deci- centi- milli- base unit kilo- hecto- deca- Example: 36 dm = ______ hm

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Practice 37 daL = _________ dL 8 mm = ________ km

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