PRE-PUBLICA TION EDITION - Nelson Education

Scientific NotationOn many calculators, scientific notation is enteredusing a special key, labelled EXP or EE. This keyincludes “×10” from the scientific notation, and youneed to enter only the exponent. For example, toenter7.5 × 10 4 press7 . 5 EXP 43.6 × 10 –3 press 3 . 6 EXP +/– 3Calculating a MeanThere are many statistical methods of analyzingexperimental evidence. One of the most commonand important is calculating an arithmetic mean,or simply a mean. The mean of a set of values is thesum of all reasonable values divided by the totalnumber of values. (This is also commonly knownCSH-F29-SHOS10SB.aias the average of a set of values, but this term is notrecommended because it is too vague and open todifferent interpretations.)Suppose you measure the root growth of fiveseedlings. Your root measurements after three daysare 1.7 mm, 1.6 mm, 1.8 mm, 0.4 mm, and 1.6 mm.What is the mean root growth? Inspection of themeasurements shows that the 0.4 mm measurementclearly does not fit with the rest. Perhaps this seedlingwas infected with a fungus, or some other problemoccurred. You should not include this result in yours Handbook mean but leave it in your evidence table so everyonecan see the decision that you made. Using only9-SHOS10SBreasonable values,Art Group mean root growth = 1.7 mm + 1.6 mm + 1.8 mm + 1.6 mmah Crowle= 1.7 mmsMeans are important in all areas of science becausemultiple measurements or trials are widely used toincrease the reliability of the results.EquationsAlgebra is a set of rules and procedures for workingwith mathematical equations. In general, yourequations will contain one unknown quantity.Whatever mathematical operation is performedto one side of an equation must be performed tothe other side. To solve for an unknown value, youneed to isolate it on one side of the equal sign. Toaccomplish this, you should follow three rules:1. The same quantity can be added or subtractedfrom both sides of the equation without changingthe equality.The following examples illustrate this rule:100 m = 100 m x + b = y100 m − 5 m = 100 m − 5 m x + b − b = y − b95 m = 95 m x = y − bThe example on the left shows the applicationof this rule using quantities with numbers andunits. The rule works equally well with quantitysymbols. The example on the right shows how toisolate x.2. The same quantity can be multiplied or dividedon both sides of the equation without changingthe equality.The following examples illustrate this rule. Theexample on the left shows the use of this rulewith known quantities. Use the same rule withan equation containing quantity symbols toisolate one of the quantities. To solve for d in theexample on the right, multiply both sides by t.Notice that t divided by t equals 1. Multiplying ordividing any quantity by 1 does not change thequantity; therefore, d × 1 = d.120 m = 120 m v = ​ d__t ​​ ______ 120 8.0 ms = ​120 ______8.0 ms ​ v × t = __ ​d t ​ × t15 m/s = 15 m/s vt = d or d = vt632 Skills Handbook NEL