The METRIC SYSTEM & CONVERSIONS Factor Label/Dimensional Analysis Review

Conversions between the U.S. Customary System and the Metric System Approximate equivalences between the U.S. Customary System and the Metric System are needed for conversion between systems Dimensional Analysis will be used to compute the conversion

Equivalences Copy this Down! Units of Weight –1 oz g –1 lb 454 g –2.2 lb 1 kg Units of Capacity –1.06 qt 1 L –1 gal 3.79 L Units of Length –1 in = 2.54 cm –3.28 ft 1 m –1.09 yd 1 m –1 mi 1.61 km

Dimensional Analysis Dimensional Analysis (also called Factor- Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value (Multiplication Property of 1 – the Magic One) Use the units to dictate the form of the Magic One

Ex: Convert 130 lbs to kg (round to the nearest whole number) Write the original measurement as a unit fraction Multiply the unit fraction by a magic one – the form of which is dictated by the units –the numerator unit is the unit you want –the denominator unit is the unit you want to eliminate Write your answer in the specified form (decimal number)

= 59 kg Ex: Convert 130 lbs to kg (round to the nearest whole number)

Ex: Convert 60 km to mi (round to the nearest whole number) Write the original measurement as a unit fraction Multiply the unit fraction by a magic one – the form of which is dictated by the units –the numerator unit is the unit you want –the denominator unit is the unit you want to eliminate Write your answer in the specified form (decimal number)

= 37.2 mi = 37 mi Ex: Convert 60 km to mi (round to the nearest whole number)

Ex: Convert 5.4 kg to lb (round to the nearest tenth place) Write the original measurement as a unit fraction Multiply the unit fraction by a magic one – the form of which is dictated by the units –the numerator unit is the unit you want –the denominator unit is the unit you want to eliminate Write your answer in the specified form (decimal number)

= lb = 11.9 lb Ex: Convert 5.4 kg to lb (round to the nearest tenth place)

Ex: Convert 45 cm to in (round to the nearest tenth place) Write the original measurement as a unit fraction Multiply the unit fraction by a magic one – the form of which is dictated by the units –the numerator unit is the unit you want –the denominator unit is the unit you want to eliminate Write your answer in the specified form (decimal number)

= in = 17.7 in Ex: Convert 45 cm to in (round to the nearest tenth place)

Ex: As a practical joke, on the show Candid Camera, a gas station listed their price as $1.79/Liter. People gassing up thought they were getting a great deal, but then were outraged when their total owed came up. WHY? What should we do? What do you notice about the listed price?

Listed their price as $1.79/Liter.

Ex: The price of a certain medication is $35 per Liter. Find the price per fluid ounce. But now what? There isn’t a direct equivalence from Liters to fluid ounces. We can use several equivalences stepping down to fluid ounces Liters  Quarts  Pints  Cups  fluid ounces