Metric Conversions - Length, Area, Volume Many people have difficulty when it comes to converting metric units of measure to some other form. This handout will go over the basics of these conversions. The Handbook of Formulae and Constants contains a chart indicating metric prefixes and the Conversion Chart for Metric Units. This shows the relationships between the various prefixes used in the SI system.

1

Referring to the “Names in the Metric System” chart, the prefix of a certain unit determines the magnitude of that unit. For example, a kilogram means one gram x 103 or 1000 grams; a millimeter means one metre multiplied by 10-3 or 1 - one thousandths of a metre. 10 megapascals equals one pascal x 106 or 10 million pascals. The prefixes you will most commonly see in this course are: giga, mega, kilo, centi, and milli. To convert from one unit to another, in the SI, system requires only that you change the decimal place of the number. For example, to convert 1.0 metre to centimeters (referring to the Conversion Chart for Metric Units), look up “metre” in the left hand column and “to centi-“ across the top. Where these two meet you will see “x 102”. This means that you multiply 1.0 metre x 102 which equals 100. To convert 23 kilograms to grams; find where “kilo” in the left hand column and “gram”, on the top, meet. Now multiply 23 kilograms by the multiplier. 23 kilograms x 103 = 23000 grams. Exercise #1 Convert the following: 1. 2. 3. 4. 5. 6.

45 millilitres to litres 600 kilopascals to pascals 30 mega-ohms to ohms 2.3 kilometres to centimetres 4530 millimetres to centimeters 870 centigrams to grams

Answers are at the end of this document.

Conversion Factors Another method of converting units is through the use of conversion factors. Under the heading of Basic Units in the Handbook of Formulae, you will see that “1 metre = 100 centimetres”. This is equal to

or

. These are known as “conversion factors”. We

can use these conversion factors because they are equal to “1” and anything multiplied by 1 equals the number itself. Convert 245 cm to metres. Here you can see that the units “cm” cancel and you are left with metres. It is important to use the correct conversion factor so that the units of the original quantity cancel.

2

Convert 4.5 litres to milliliters

Let’s use the incorrect conversion factor first.

This answer is obviously not correct, no units can cancel and we are left with nonsense units. Using the correct conversion factors leads to an equation that looks like this: , again the “L’s” cancel and you are left with the units that you want, namely milliliters.

Converting areas and volumes (m2, cm2) using conversion factors is quite simple using the basic conversion factors. For example, convert 1 square meter to square centimeters. We know that one square metre is 1m x 1m = 1 m2. Using the conversion factor for metres and centimeters which is (

)

, we can form an equation as follows: (

)

Note that the conversion factor is squared since we are dealing with area. Convert 368500 cm3 to m3 (

)

(

)

Exercise #2 Referring to the Handbook of Formulae, convert the following: 1. 2. 3. 4. 5. 6.

3.5 miles to feet 48890 mm to metres 16.8 m2 to cm2 5400 cm3 to mm3 55 m2 to mm2 23550 L to m3 3

Answers are at the end of this document. Exercise #3 These conversions will take more than one step, and depending on the conversion factors used, a slightly different answer may be arrived at. 1. 2. 3. 4. 5. 6.

23 km to yards 17 km2 to acres 2.5 m3 to in3 7.71 tonnes to long tons 440 in3 to litres 6.5 m to inches

Answers are at the end of this document. Important Note: When converting to area or volume, etc. it is important to remember that you must square or cube the conversion factor (for area and volume respectively) and not merely use the basic conversion factor. A common error is simply moving the decimal place in accordance with the conversion factor. Example: A strut has an area of 35 cm2. It carries a load of 750 kg. What is the stress in the strut? In this type of problem the area of the strut must be expressed in square metres. Because there are 100 cm in one metre, many people will only move the decimal place over 2 spots to convert but that is incorrect…35 cm2 is not equal to 0.35 m2 Using the conversion factor you see that

(

)

Or Using the Conversion Chart for Metric Units (

)

(

)

Exercise #4 - Word Problems 1. A tank measures 3.5m x 4m x 1.25m. The flow meter on the line used to fill the tank is calibrated in US gallons. How may US gallons will it take to fill the tank? 2. You are driving in the States. A sign ahead says “Sacramento 90 miles”. How many kilometers is this? 3. A full pail of sodium sulphite holds 20 litres of the chemical. The mass of chemical is 1.561 grams per cm3. The pail has a mass of 0.56 kg. What is the mass of the full pail in kilograms? 4

4. A train is travelling at 95 km/hour. What is this speed in metres/second? 5. A pressure vessel is in the form of a cylinder with flat ends. The diameter is 79 cm and the length is 2350 mm. What is the volume in m3? 6. What is the displacement of a Chrysler 440 cu in. engine in litres? 7. There are 640 acres in one section of land. How many hectares is this? 8. A flat piece of sheet metal is 0.75m x 1.1m. Two circles are to be cut out of the metal. One circle is 115 mm in diameter. The other is 25.3 cm in radius. How much sheet metal will be left in square metres? 9. A tank has a volume of 4.65 m3. How many imperial gallons does it hold? 10. A boiler holds a 4.15 tonnes of water. It takes 45 minutes to fill the boiler. What is the flow rate in US gallons per minute? (Refer to the “Useful Data” section of the Handbook of Formulae for the mass of fresh water) 11. A landscaping company delivers and spreads 25 “yards” of topsoil. How many cubic metres of dirt is this. (Note: one “yard” of soil is a volume equal to 1 yard x 1 yard x 1 yard) 12. What pressure is generated (in kilopascals) if a force of 560 newtons is applied to an area of 43 mm2? Note: Pressure (Pa) =

(

( ) )

Answers are at the end of this document.

Answers Exercise #1 1. 2. 3. 4. 5. 6.

0.045 L 600 000 Pa 30 000 000 ohm 230 000 cm 453 cm 8.7 grams

Exercise #2 1. 2. 3. 4. 5. 6.

18 480 ft 48.890 m 0.00168 m2 5 400 000 mm3 55 x 106 mm2 23.55 m3

Exercise #3 1. 25 142.86 yds 5

2. 3. 4. 5. 6.

4200.77 acres 152 439 in2 7.57 long tons 7.2 L 255.84 in.

Exercise #4 – Word Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

4629.63 US gal 145 km 31.78 kg 26.389 m/s 1.15 m3 7.2 L 259.2 ha 0.614 m2 1025 imp. Gallon 24.4 USgal/min 20.65 m3 13 023 kPa

6