Conversions: aka Dimensional Analysis

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

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

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

Standard System 88 different types of units 88 different types of units hundreds of conversions. hundreds of conversions.

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

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

Metric Prefixes TeraT10 12 TeraT10 12 GigaG10 9 GigaG10 9 MegaM10 6 MegaM10 6 Kilo k 10 3 Kilo k 10 3 (Fill in your chart) decid10 -1 centic millim10 -3 microμ10 -6 nanon10 -9 picop

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

Conversions How about a harder one? How many minutes are in hours? How about a harder one? How many minutes are in hours? Since you can’t do this in your head, you must think and use the same method you used before. Since you can’t do this in your head, you must think and use the same method you used before minutes minutes

Dimensional Analysis Convert 14.3 cm to meters: Convert 14.3 cm to meters: 14.3 cm |________ 14.3 cm |________ l l Write your t bar and add the given with its label. Write your t bar and add the given with its label.

Dimensional Analysis Convert 14.3 cm to meters: Convert 14.3 cm to meters: 14.3 cm |________ 14.3 cm |________ l cm l cm Add the units given on the t bar so that they will cancel out. Add the units given on the t bar so that they will cancel out.

Dimensional Analysis Convert 14.3 cm to meters: Convert 14.3 cm to meters: 14.3 cm |______m_ 14.3 cm |______m_ l cm l cm Add the units you are trying to get to. Add the units you are trying to get to.

Dimensional Analysis Convert 14.3 cm to meters: Convert 14.3 cm to meters: 14.3 cm |___1 ___m_ 14.3 cm |___1 ___m_ l 100 cm l 100 cm Fill in the conversion. Fill in the conversion.

Dimensional Analysis Convert 14.3 cm to meters: Convert 14.3 cm to meters: cm- |___1 ___m_ = cm- |___1 ___m_ = l 100 -cm- l 100 -cm- Cancel units and do the math. Cancel units and do the math x 1 ÷ 100 =.143 m 14.3 x 1 ÷ 100 =.143 m

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

Multiple Steps If it takes 2 or more conversions. (Folders!) If it takes 2 or more conversions. (Folders!) g in 3.1 lbs? 1 lb = 16 oz; g in 3.1 lbs? 1 lb = 16 oz; 1 oz = g 1 oz = g 3.1 –lbs- l 16 –oz- l g = ? 3.1 –lbs- l 16 –oz- l g = ? l 1 -lb- l 1 –oz- l 1 -lb- l 1 –oz- ( 3 x 16 x ) = 1.75 = 1.8 g ( 3 x 16 x ) = 1.75 = 1.8 g

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