Conversions aka Dimensional Analysis The Metric System n

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 hundreds of conversions.

Metric System n Only 3 base units n 10 standard prefixes n Only one set of conversions to learn. The one set works for everything.

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

Metric Prefixes n Tera T n Giga G n Mega M n Kilo k 1012 109 106 103 (Fill in your chart) n deci d n centi c n milli m n micro μ n nano n n pico p 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12

Conversions n How many minutes are in 3 hours? n 180 minutes! n Many of you knew can do this in your head, instinctively. n To get the answer, you used a CONVERSION FACTOR (60 min = 1 hour. )

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 275. 8 minutes

Dimensional Analysis n Convert 14. 3 cm to meters: n n 14. 3 cm |____ l Write your t bar and add the given with its label.

Dimensional Analysis n Convert 14. 3 cm to meters: n n 14. 3 cm |____ l cm Add the units given on the t bar so that they will cancel out.

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

Dimensional Analysis n Convert 14. 3 cm to meters: n n 14. 3 cm |___1 ___m_ l 100 cm Fill in the conversion.

Dimensional Analysis n Convert 14. 3 cm to meters: n n n 14. 3 -cm- |___1 ___m_ l 100 -cm- = Cancel units and do the math. 14. 3 x 1 ÷ 100 =. 143 m

Dimensional Analysis n There are some cases that have special rules: Multiple steps n Units in the denominator n

Multiple Steps n n n If it takes 2 or more conversions. (Folders!) g in 3. 1 lbs? 1 lb = 16 oz; 1 oz = 0. 0353 g n 3. 1 –lbs- l 16 –ozl 1 -lb- n ( 3 x 16 x 0. 0353 ) = 1. 75 = 1. 8 g n l 0. 0353 g = l 1 –oz- ?

Units “per” (Miles per hour) n If you read a unit “per ____”, then it goes on the bottom (denominator. ) Its conversion goes UP and across, so you cancel. 35 mil l 1 hr l 1 min = ? hr l 60 min l 60 sec (35 ÷ 60 ) = 0. 09722222 = 0. 097 miles per sec n