1 2.2. Mass and length Mass and length are fundamental quantities in the International System of Units. Their SI units are the kilogram (kg ) and the metre (m). However, it is also ver y common to measure mass in grams (g ). Quantity SI unit Symbol Mass Kilogram Kg Length Metre m The table below also shows the multiples and submultiples we will use. Name Symbol Factor Unit (mass) Unit (length) Multiple kilo k × 103 kg km hecto h × 102 hg hm deca da × 10 dag dam Base unit g m Submultiple deci d × 10-1 dg dm centi c × 10-2 cg cm milli m × 10-3 mg mm The factor in the table represents the relationship between the multiple or submultiple and the unit. Obser ve what these factors mean . Powers Powers are a mathematical operation in which a number is multiplied by itself several times. The power 83 is read as "eight to the power of three" and it is represented as: 83 = 8 × 8 × 8 Negative exponent powers are the inverse of positive exponent powers. 8 1 8 1 8 8 8 3 3 − = = ⋅ ⋅ To raise a power to another power, we multiply the exponents: 8 8 8 2 3 2 3 6 ( ) = = ⋅ base exponent times 3 times 3 13 Complete this table in your notebook: Symbol Unit Symbol Unit mg … … decilitre km … … millimetre … centimetre hg … … millimetre dag … 14 Take a milk carton and measure its height, width and length with a ruler. a) Write the result in cm, mm and m. b) Calculate the dimensions of a package containing six milk cartons. Write it in cm, mm and m. 15 A foot is a measurement of length based on the human foot. Using your foot as the unit of measurement, measure the length of the whiteboard and write down the result. a) If you had used this unit of measurement last year, would you have obtained the same result? What if you used it next year? b) Does wearing shoes affect the result? c) Look for information about the distance that is equal to a foot. Has it been the same throughout history? d) Is it appropriate to use the foot as a unit of measurement? Compare it with the metre. A C T I V I T I E S Multiples 101 = 10 102 = 100 103 = 1000 ten hundred thousand 2 zeros 3 zeros 1 zero Submultiples 10-1 = 1 10 = 0.1 10-2 = 1 102 = 1 100 = 0.01 10-3 = 1 103 = 1 1 000 = 0.001 tenth hundredth thousandth 1 zero 2 zeros 3 zeros 15
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