In addition to using proportional ratios to make conversions between units of currency or units of measure (English to metric, etc), a process known as Dimensional Analysis can be used.

Since 12 inches is equivalent to 1 foot, then the ratios: , are each equivalent to 1, since they represent a length divided by an identical length. Thus, if you multiply any length quantity by either of these ratios, it does not change the objects length, only the units it is measured in. If 72 inches is multiplied by : Note: that the units of inch cancel in the numerator and denominator, and the remaining unit is feet, and 72/12 reduces to 6. These ratios are called unit conversion ratios, since they are used for conversion between different units of measure. How do you know which ratio to pick? Choose the one with the denominator unit the same as the unit of the quantity you are converting from, to cause those units to cancel.

Convert 30 ft to inches:

This process is called dimensional analysis, since it helps you convert quantities to the correct dimension or measurement unit.

This process may also be used to convert between different units of measure for areas and volumes.

How many tiles, that are 1in x 2in (2 in²), do you need to tile a 6ft x 8ft bathroom floor? The area of the bathroom is 6 x 8 = 48 ft². . Divide the area of the floor by the area of 1 tile to determine the number of tiles needed. Note; the square inches cancelled, leaving the answer in tiles.

A Honda engine has a cylinder volume displacement of 2.0 liter (2,000cm³). What is its displacement in cubic inches?

Dimensional analysis can also be used to perform multiple unit conversions. Convert 100 yards to meters, using: 1 inch = 2.54 cm and 100 cm = 1 m.

PRACTICE:

When runners talk about a "10k", they are refering to a 10 kilometer run. How many miles is a "10k"; if 1 km = 1,000 m, 1 yd = 0.9144 m, and 5,280 ft = 1 mile? Ans: 6.21 mi

CONVERTING QUANTITIES WITH MIXED UNITS: Convert 30 mpg to kpl (kilometers per liter); using 1 mi = 1.609 km, 1 gal = 3.785 l.

or 12.75kpl

How much does a waterbed weigh that is 6.5 ft long by 5 ft wide by 1 ft thick. You start by weighing a gallon milk jug of water and find that the water in the jug weighs 8.34 lbs. You lookup, in a conversion table, and find that 1 gallon is 231 cubic inches. The volume of the bed is in cubic feet (6.5ft x 5ft x 1 ft = 32.5 ft³). First convert 231 in³ to ft³:

Next find the weight of 1 cubic foot of water:

Now multiply the volume of the bed by the weight of water per cubic foot:

or just over 1 ton! No wonder they are so hard to move.

PRACTICE: Use the conversion values inside the back cover of your text.

1) Convert 12 kg to pounds and ounces. (1lb = 16oz) Ans: 26lb 6.4oz

2) Find the area, in square inches, of a 35mm slide. It measures 35mm x 35 mm (3.5cm x 3.5cm). Ans: 1.9 in²

3) Convert a tire pressure of 30 psi (pounds per square inch) to kilograms per square

centimeter. Ans: 2.1 kg/cm²