III. THE METRIC SYSTEM

Recall…• 2 parts

• A number and a unit

• Units = what was measured

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”

B. SI Base Units• Length (distance) :

• Mass :

• Volume :

• Time :

meter (m)

gram (g)

Liters (L)

second (s)

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

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

D. Exponent Review•10x

• 10 = base• x = exponent; tells how many times 10 is multiplied by itself• 102 = 10 x 10 = 100

•10-x =

• 10-2 = = =

_1_ 10x

_1_ 102

_1_ 100

0.01

D. Exponent Review Cont.• If the exponent is POSITIVE , the number is larger than 1• 103 is 1000 (1 with 3 zeroes)• 105 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)

Name Symbol Numerical Value Power of Ten

mega- M 1,000,000 106

kilo- k 1,000 103

hecto- h 100 102

deca- da 10 101

Base Units meters (m),liters (L),

grams (g),seconds (s)

100

deci d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- µ 0.000001 10-6

E. Metric Prefixes

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)

Practice

What is the prefix?

1. µ2. m3. h4. c

5. da6. k7. d8. M

F. Metric Conversions (Math/AP way)• Step 1: Identify powers of 10 for each prefix

• Base unit with no prefix = 100

• 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: 100 mL: 10-3

Subtract exponents: 0 – (-3) = +3 Move decimal 3 places to the right

1600

F. Metric Conversions (Math/AP way)• Step 1: Identify powers of 10 for each prefix

• Base unit with no prefix = 100

• 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: 103

Subtract exponents: -2 – (3) = -5 Move decimal 5 places to the left

0.0000254

Practice• 1000 mg = _______ g

• 0.15 hm = _________ mm

G. Metric Conversions (Easy Way)

deci-(drinking)

centi-(chocolate)

milli-(milk)

base unit(by)

kilo-(king)

hecto-(henry)

deca-(died)

Example: 36 kg = ______ cg

G. Metric Conversions (Easy Way)

deci-

centi-

milli-

base unit

kilo-

hecto-

deca-

Example: 36 dm = ______ hm

Practice• 37 daL = _________ dL

• 8 mm = ________ km