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The METRIC SYSTEM & CONVERSIONS

The METRIC SYSTEM & CONVERSIONS. MSJC ~ San Jacinto Campus Math Center Workshop Series Janice Levasseur. The Metric System. The metric system is an internationally standardized system of units of measurement. The metric system is based on a base unit and prefixes. Prefixes.

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The METRIC SYSTEM & CONVERSIONS

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  1. The METRIC SYSTEM & CONVERSIONS MSJC ~ San Jacinto Campus Math Center Workshop Series Janice Levasseur

  2. The Metric System • The metric system is an internationally standardized system of units of measurement. • The metric system is based on a base unit and prefixes.

  3. Prefixes • Kilo - 1000 k • Hecto - 100 h • Deca - 10 da • 1 • Deci - 0.1 d • Centi - 0.01 c • Milli - 0.001 m

  4. 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

  5. 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

  6. 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 x 1cm • 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

  7. 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 x 10 cm • Metric Units of Capacity • Kiloliter (kL) = 1000 L • Hectoliter (hL) = 100 L • Decaliter (daL) = 10 L • Liter (L) = 1 L • Deciliter (dL) = 0.1 L • Centiliter (cL) = 0.01 L • Milliliter (mL) = 0.001 L

  8. 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

  9. 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 • 1600 cm = 16.00 m

  10. Ex: Convert 2 kL to L • kL hL daL L dL cL mL • Move 3 places to the right to get from kL to L • Therefore, move the decimal point in 2 three places to the right to convert from kL to L • 2 KL = 2000 L

  11. 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 • 241 g = 241,000 mg

  12. Ex: Convert 3 mL to L • kL hL daL L dL cL mL • Move 3 places to the left to get from mL to L • Therefore, move the decimal point in 3 three places to the left to convert from mL to L • 3 mL = 0.003 L

  13. 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 • 45 cm = 0.00045 km

  14. 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 • 5.4 kg = 54000 dg

  15. 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

  16. 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 m • 1 mi 1.61 km

  17. 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

  18. 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)

  19. Ex: Convert 130 lbs to kg (round to the nearest whole number) = 59.0 kg

  20. 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)

  21. Ex: Convert 60 km to mi (round to the nearest whole number) = 37.2 mi = 37 mi

  22. 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)

  23. Ex: Convert 5.4 kg to lb (round to the nearest tenth place) = 11.88 lb = 11.9 lb

  24. 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)

  25. Ex: Convert 45 cm to in (round to the nearest tenth place) = 17.71 in = 17.7 in

  26. 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?

  27. Listed their price as $1.79/Liter.

  28. 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

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