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The Metric System & Unit Conversions: aka Dimensional Analysis

The Metric System & Unit Conversions: aka Dimensional Analysis. The Metric System. In America, we use the standard system of units (pounds, ounces, miles, feet, etc) In Science, and in all other countries, a different system is used called the metric system. The Metric System.

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The Metric System & Unit Conversions: aka Dimensional Analysis

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  1. The Metric System & Unit Conversions: aka Dimensional Analysis

  2. The Metric System • In America, we use the standard system of units • (pounds, ounces, miles, feet, etc) • In Science, and in all other countries, a different system is used called the metric system.

  3. The Metric System • The U.S. will probably switch to it in your lifetimes because: • U.S. is the ONLY major nation not using it. • Easier trade and communication • It is a decimal system (like our money) and much easier to use.

  4. Metric VS Standard • Neither is more ACCURATE, just different.

  5. Standard System • 88 different types of units • Even most Americans can’t name more than a dozen • hundreds of conversions. • Most American citizens know very few.

  6. Metric System • Only 7 base units • Second s time • kilogram kg mass • ° kelvin K temperature • meter m distance • candle c light • ampere A current and resistance • mole mol amount of substance • 10 common prefixes (20 total) • Only one set of conversions to learn. The one set works for everything.

  7. Most Common Metric Base Units • Length • Meters (m) • Mass – (weight) • Grams (g) • Volume • Liters (L)

  8. Metric Prefixes That make the base unit BIGGER

  9. Metric Prefixes That make the base unit SMALLER

  10. Unit Conversions • How many minutes are in 3 hours? • 180 minutes! • Many of you knew this already or can do it in your head, instinctively. • To get the answer, you needed two things: • CONVERSION FACTOR (60 min = 1 hour.) • Know to DIVIDE or MULTIPLY.

  11. Unit Conversions • How about a harder one? How many minutes are in 4.597 hours? • Since you can’t do this in your head, you must think and use the same method you used before. • We will use a system called the factor-label method, or Dimensional Analysis. • 275.8 minutes

  12. Dimensional Analysis – Step 1 • Convert 14.3 cm to meters: • ______|________ • l • Write your t-chart.

  13. Dimensional Analysis – Step 2 • Convert 14.3 cm to meters: • 14.3cm |________ • l • Add the given with its label. • (IE – the number the problem gives you and its UNIT)

  14. Dimensional Analysis – Step 3 • Convert 14.3 cm to meters: • 14.3 cm |________ • l cm • Add the units of the given on the t-chart. • It will go DIAGONALLY from the original. • This is so the units will cancel out later.

  15. Dimensional Analysis – Step 4 • Convert 14.3 cm to meters: • 14.3 cm |______m_ • l cm • Add the unit you are trying to get to.

  16. Dimensional Analysis • Convert 14.3 cm to meters: • 14.3 cm |___1 ___m_ • l 100 cm • Fill in the conversion factor that links the two units. • EX: 1 m = 100 cm • (you will usually need to look this up.)

  17. Dimensional Analysis • Convert 14.3 cm to meters: • 14.3 -cm- |___1 ___m_ = • l 100 -cm- • Cancel units and do the math. • MATH: • Multiply if the number is on the top • Divide if the number is on the bottom 14.3 x 1 ÷ 100 = 0.143 m

  18. How to Solve a Dimensional Analysis Problem • Your notes have a fully worked example problem. • We will go over it now. • Note the location of this page. • Use it as a reference for future problems.

  19. Temperature :K vs °C vs °F

  20. Temperature Conversions • °C & K are the metric units for temp. • [K] = [°C] + 273.15 • °F is the standard unit for temp. • To convert between °C and °F: OR

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