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. Fill in 1st and 2nd blanks in the notes

The Metric System U.S. is the ONLY major nation not using it. 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.

Metric VS Standard Neither is more ACCURATE, just different. Fill in 3rd blank in notes.

Standard System 88 different types of units hundreds of conversions. Even most Americans can’t name more than a dozen hundreds of conversions. Most American citizens know very few. Fill in the 2 boxes under the title STANDARD in the notes.

Metric System Only 7 base units 10 common prefixes (20 total) 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. Fill in the two boxes labeled METRIC in the notes.

Most Common Metric Base Units Length Meters (m) Mass – (weight) Grams (g) Volume Liters (L) As each of the three base units fill in, do the appropriate PRACTICE question in the notes as a class.

That make the base unit BIGGER Metric Prefixes That make the base unit BIGGER

Meaning (multiply by): Prefix: Symbol S. N. Meaning (multiply by): Yotta- Y 1024 1 000 000 000 000 000 000 000 000 Zetta- Z 1021 1 000 000 000 000 000 000 000 Exa- E 1018 1 000 000 000 000 000 000 Peta- P 1015 1 000 000 000 000 000 Tera- T 1012 1 000 000 000 000 Giga- G 109 1 000 000 000 Mega- M 106 1 000 000 kilo- k 103 1000 hecto- h 102 100 deka- da 10 Have the students fill in the SYMBOL and SCIENTIFIC NOTATION in their notes. Have them fill in the SN with the format 1x1024, etc.

That make the base unit SMALLER Metric Prefixes That make the base unit SMALLER

deci- d 10-1 0.1 centi- c 10-2 0.01 milli- m 10-3 0.001 micro- µ (mu) Prefix: Symbol S. N. Meaning (Multiply by) deci- d 10-1 0.1 centi- c 10-2 0.01 milli- m 10-3 0.001 micro- µ (mu) 10-6 0.000 001 nano- n 10-9 0.000 000 001 pico- p 10-12 0.000 000 000 001 femto- f 10-15 0.000 000 000 000 001 atto- a 10-18 0.000 000 000 000 000 001 zepto- z 10-21 0.000 000 000 000 000 000 001 yocto- y 10-24 0.000 000 000 000 000 000 000 001 Have the students fill in the SYMBOL and SCIENTIFIC NOTATION in their notes. Have them fill in the SN with the format 1x1024, etc.

Unit Conversions 180 minutes! 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. Class discussion.

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 Work this problem very quickly on the board to show the students the dimensional analysis process.

Dimensional Analysis – Step 1 Convert 14.3 cm to meters: ______|________ l Write your t-chart. No blanks in notes, just have students watch & learn this problem.

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

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.

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.

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.)

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

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. Go over the example problem in the notes.

Temperature : K vs °C vs °F kelvins degrees celsius degrees fahrenheit symbol °K °C °F boiling point of water 373.15 100. 212. average human body temperature   37. 98.6 average room temperature 20. to 25. 68. to 77. freezing point of water 273.15 0. 32. absolute zero -273.15 -459.67

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