UNIT 1 MASS AND LENGTH

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1 UNIT 1 MASS AND LENGTH Typical Units Typical units for measuring length and mass are listed below. Length Typical units for length in the Imperial system and SI are: Imperial SI inches ( ) centimetres ( ) feet ( ) metres ( ) miles ( ) kilometres ( ) The SI base unit for length is the metre. Mass Typical units for mass in both systems are: Imperial SI ounce ( ) gram ( ) pound ( ) kilogram ( ) ton ( ) tonne ( ) The SI base unit for mass is the gram mass and length 10

2 Example 1. Mass of a PC 2. Mass of a bag of chips 3. Diameter of a loonie 4. Distance from Hamilton to Toronto SI Units The SI is a modification of the metric system and is based on powers of 10. SI Prefixes The table lists common prefixes, symbols and units for length and mass. Prefix Symbol Length Mass kilo hecto deca base unit metre gram deci centi milli When a measurement is small then a fraction of the base unit is used. The width of this page could be stated in centimetres. When the measurement is large then the base unit is multiplied by a power of 10. The distance between cities would be measured in kilometres. 1- mass and length 11

3 SI Equivalencies To convert SI units, statements of equivalence are used and can be obtained from the relationship between each prefix and the base unit. The following tables list equivalencies for length and for mass. Each equivalency is relative to a base unit, the metre or the gram. Length Prefix kilo Relation to the metre (base unit of Length ) hecto deca base metre deci centi milli 1- mass and length 12

4 Mass Prefix kilo Relation to the gram (base unit of Mass) hecto deca base gram deci centi milli While all prefixes are valid, only certain ones are commonly used in practice. 1- mass and length 13

5 Unit Ratios From each statement of equivalence two unit ratios can be written. Consider the equivalence: 1 metre = 100 cm If 1 m = 100 cm If 100 cm = 1 m The ratio equals 1 The ratio equals 1 Unit ratios are used in converting units. 1- mass and length 14

6 Example For each statement of equivalence write the two unit ratios cm = 10 mm 3. 1 kg = 1000 g 2. 1 g = 1000 mg 4. 1 m = 100 cm SI Conversions The process of converting units involves multiplying the original measurement by a unit ratio to obtain the desired unit. Recall that a unit ratio has a value of 1. Multiplying by "1" does not change the measurement; however the magnitude changes to match the new units. The examples illustrate the conversion technique for using the unit ratios obtained from equivalencies. 1- mass and length 15

7 Converting Length Units Identify and use an appropriate unit ratio to convert: km to m mm to cm m to mm cm to km cm to m hm to mm 1- mass and length 16

8 Converting Mass Units Identify and use an appropriate unit ratio to convert: mg to g g to kg cg to mg g to cg g to mg kg to mg 1- mass and length 17

9 Imperial Units Before Canada adopted the SI, the Imperial system of units was used. Some industries still use the Imperial system and conversions between the two are necessary. Equivalencies Converting units in the Imperial or British system requires a list of equivalencies since there is no "10" factor as exists for SI. These equivalencies are available from conversion tables published in various forms. The table below lists a few equivalencies that will be needed in the examples following. Length Mass 12 in = 1 ft 1 pound = 16 ounces 1 mile = 5280 ft 1 ton = 2000 lb 1 yard = 36 in 3 ft = 1 yard Many more equivalencies are listed in the Appendix. 1- mass and length 18

10 Unit Ratios Write two unit ratios for each of the following: 1. 1 pound = 16 ounces 2. 1mile = 5280 feet Conversions Convert the following using unit ratios from the equivalencies listed on the previous page ft to in in to miles oz to lb yd to in 1- mass and length 19

11 Imperial/SI Conversions This section discusses the use of equivalencies to convert between the systems. Equivalencies When converting between the two systems the equivalencies must be obtained from conversion tables such as those listed in the Appendix. This table lists several common equivalencies. Length Mass 1 in = 2.54 cm 1 pound = g 1 ft = m 1 oz = g 1 mile = km 1 kg = lb 1 yd = m 1- mass and length 20

12 Unit Ratios Write the two unit ratios for each of the following: 1. 1 foot = m 3. 1 mile = km 2. 1 oz = g 4. 1 kg = lb Conversions Convert each of the following using unit ratios from the equivalencies listed on the previous page or in the Appendix miles to km cm to in 1- mass and length 21

13 3. 10 lb to kg tons to g m to yd cm to mi g to pounds oz to mg 1- mass and length 22

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