The Metric System Unit Conversions aka Dimensional Analysis

The Metric System & Unit Conversions: aka Dimensional Analysis

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

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

Metric VS Standard n Neither is more ACCURATE, just different.

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

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

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

Metric Prefixes That make the base unit BIGGER

Prefix: Symbol S. N. Meaning (multiply by): Yotta- Y 1024 1 000 000 Zetta- Z 1021 1 000 000 Exa- E 1018 1 000 000 000 Peta- P 1015 1 000 000 000 Tera- T 1012 1 000 000 Giga- G 109 1 000 000 Mega- M 106 1 000 kilo- k 103 1000 hecto- h 102 100 deka- da 10 10

Metric Prefixes That make the base unit SMALLER

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. 000 001 pico- p 10 -12 0. 000 000 001 femto- f 10 -15 0. 000 000 001 atto- a 10 -18 0. 000 000 000 001 zepto- z 10 -21 0. 000 000 000 001 yocto- y 10 -24 0. 000 000 001

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

Unit Conversions n How about a harder one? How many minutes are in 4. 597 hours? n Since you can’t do this in your head, you must think and use the same method you used before. n We will use a system called the factor-label method, or Dimensional Analysis. n 275. 8 minutes

Dimensional Analysis – Step 1 n Convert 14. 3 cm to meters: ______|____ l n Write your t-chart. n n n

Dimensional Analysis – Step 2 n Convert 14. 3 cm to meters: 14. 3 cm |____ l n Add the given with its label. n n (IE – the number the problem gives you and its UNIT)

Dimensional Analysis – Step 3 n n n n 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 n Convert 14. 3 cm to meters: 14. 3 cm |______m_ l cm n Add the unit you are trying to get to. n n n

Dimensional Analysis n n n n 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 n n n 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 n Divide if the number is on the bottom n 14. 3 x 1 ÷ 100 = 0. 143 m

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

Temperature : K vs °C vs °F temperature 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 0. -273. 15 -459. 67

Temperature Conversions n °C & K are the metric units for temp. n n [K] = [°C] + 273. 15 °F is the standard unit for temp. To convert between °C and °F: OR n