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 28.35 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)

22130

221

1130

.kg

lbs.kglbs

= 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)

61160

6111

160

.mi

km.mikm

= 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)

18811

122

145 lb.

kglb.kg.

= 11.88 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)

54245

5421

145

.in

cm.incm

= 17.71 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.

galL.

L.$

1793

1791

gal.$

1786

Ex: The price of a certain medication is $35 per Liter.

Find the price per fluid ounce.

L$135

qt.L0611

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

ptqt21

Cpt21

ozflC

81

ozfl.$923335

ozfl/.$ 031