The International System aka The METRIC SYSTEM CONVERSIONS

The International System aka The METRIC SYSTEM & CONVERSIONS

The Metric System • The metric system is an internationally standardized system of units of measurement. Its correct name is International System of Measurements. • The metric system is based on a base unit and prefixes.

Prefixes • • Kilo Hecto Deca Deci Centi Milli - 1000 10 1 0. 01 0. 001 k h da d c m

Length • The basic unit of length in the metric system is the meter (m) • Metric Units of Length – – – – Kilometer (km) = 1000 m Hectometer (hm) = 100 m Decameter (dam) = 10 m Meter (m) = 1 m Decimeter (dm) = 0. 1 m Centimeter (cm) = 0. 01 m Millimeter (mm) = 0. 001 m

Mass • Weight is a measure of how strongly gravity is pulling on an object (decreases as elevation increases) • Mass is the amount of material in an object (doesn’t change) • Note: on Earth, weight and mass are used interchangeably

Mass • The basic unit of mass in the metric system is a gram (g) • 1 g = mass of water in a cube that measures 1 cm x 1 cm • Metric Units of Mass – – – – Kilogram (kg) = 1000 g Hectogram (hg) = 100 g Decagram (dag) = 10 g Gram (g) = 1 g Decigram (dg) = 0. 1 g Centigram (cg) = 0. 01 g Milligram (mg) = 0. 001 g

Capacity • Liquid substances are measured in units of capacity. • The basic unit of mass in the metric system is a liter (L) • 1 L = capacity of a cube that measures 10 cm x 10 cm • Metric Units of Capacity – – – – Kiloliter (k. L) = 1000 L Hectoliter (h. L) = 100 L Decaliter (da. L) = 10 L Liter (L) = 1 L Deciliter (d. L) = 0. 1 L Centiliter (c. L) = 0. 01 L Milliliter (m. L) = 0. 001 L

Conversions within the Metric System • To convert units within the metric system, write the prefixes in order from largest to smallest k h da d c m • To convert from a smaller unit to a larger unit, move to the left • To convert from a larger unit to a smaller unit, move to the right

Ex: Convert 1600 cm to m • km hm dam m dm cm mm • Move 2 places to the left to get from cm to m • Therefore, move the decimal point in 1600 two places to the left to convert from cm to m Ø 1600 cm = 16. 00 m

Ex: Convert 2 k. L to L • k. L h. L da. L L d. L c. L m. L • Move 3 places to the right to get from k. L to L • Therefore, move the decimal point in 2 three places to the right to convert from k. L to L Ø 2 KL = 2000 L

Ex: Convert 241 g to mg • kg hg dag g dg cg mg • Move 3 places to the right to get from g to mg • Therefore, move the decimal point in 241 three places to the right to convert from g to mg Ø 241 g = 241, 000 mg

Ex: Convert 3 m. L to L • k. L h. L da. L L d. L c. L m. L • Move 3 places to the left to get from m. L to L • Therefore, move the decimal point in 3 three places to the left to convert from m. L to L Ø 3 m. L = 0. 003 L

Ex: Convert 45 cm to km • km hm dam m dm cm mm • Move 5 places to the left to get from cm to km • Therefore, move the decimal point in 45 five places to the left to convert from cm to km Ø 45 cm = 0. 00045 km

Ex: Convert 5. 4 kg to dg • kg hg dag g dg cg mg • Move 4 places to the right to get from kg to dg • Therefore, move the decimal point in 5. 4 four places to the right to convert from kg to dg Ø 5. 4 kg = 54000 dg

Conversions between the U. S. Customary System and the Metric System • Approximate equivalences between the U. S. Customary System and the Metric System are needed for conversion between systems • Dimensional Analysis will be used to compute the conversion

Equivalences • Units of Weight – 1 oz 28. 35 g – 1 lb 454 g – 2. 2 lb 1 kg • Units of Capacity – 1. 06 qt 1 L – 1 gal 3. 79 L • Units of Length – – 1 in = 2. 54 cm 3. 28 ft 1 m 1. 09 yd 1 mi 1. 61 km

Dimensional Analysis • Dimensional Analysis (also called Factor. Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value (Multiplication Property of 1 – the Magic One) • Use the units to dictate the form of the Magic One

Ex: Convert 130 lbs to kg (round to the nearest whole number) • Write the original measurement as a unit fraction • Multiply the unit fraction by a magic one – the form of which is dictated by the units – the numerator unit is the unit you want – the denominator unit is the unit you want to eliminate • Write your answer in the specified form (decimal number)

Ex: Convert 130 lbs to kg (round to the nearest whole number) = 59. 0 kg

Ex: Convert 60 km to mi (round to the nearest whole number) • Write the original measurement as a unit fraction • Multiply the unit fraction by a magic one – the form of which is dictated by the units – the numerator unit is the unit you want – the denominator unit is the unit you want to eliminate • Write your answer in the specified form (decimal number)

Ex: Convert 60 km to mi (round to the nearest whole number) = 37. 2 mi = 37 mi

Ex: Convert 5. 4 kg to lb (round to the nearest tenth place) • Write the original measurement as a unit fraction • Multiply the unit fraction by a magic one – the form of which is dictated by the units – the numerator unit is the unit you want – the denominator unit is the unit you want to eliminate • Write your answer in the specified form (decimal number)

Ex: Convert 5. 4 kg to lb (round to the nearest tenth place) = 11. 88 lb = 11. 9 lb

Ex: Convert 45 cm to in (round to the nearest tenth place) • Write the original measurement as a unit fraction • Multiply the unit fraction by a magic one – the form of which is dictated by the units – the numerator unit is the unit you want – the denominator unit is the unit you want to eliminate • Write your answer in the specified form (decimal number)

Ex: Convert 45 cm to in (round to the nearest tenth place) = 17. 71 in = 17. 7 in

Ex: As a practical joke, on the show Candid Camera, a gas station listed their price as $1. 79/Liter. People gassing up thought they were getting a great deal, but then were outraged when their total owed came up. WHY? • What do you notice about the listed price? • What should we do?

Listed their price as $1. 79/Liter.

Ex: The price of a certain medication is $35 per Liter. Find the price per fluid ounce. But now what? There isn’t a direct equivalence from Liters to fluid ounces. We can use several equivalences stepping down to fluid ounces Liters Quarts Pints Cups fluid ounces