MEASUREMENT AND CALCULATIONS Chapter 9.2. ► Why is it important to be accurate?  Drug design  Construction  Sports.

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Presentation transcript:

MEASUREMENT AND CALCULATIONS Chapter 9.2

► Why is it important to be accurate?  Drug design  Construction  Sports

Example ► At the 2008 Olympics, Usain Bolt and Asafa Powell were very close. ► They both registered times of 9.7 seconds.  How are significant digits important here? ► Usain’s time was 9.69s, Asafa’s was 9.72s

Significant Digits ► The international agreement about the correct way to record measurements. ► The number of significant digits in your answer is important because depending on your method of measurement, you can only be certain to a specific place value. ► Ex. You time a foot race with an analog clock. Can you be certain of the winner?

► Significant digits allow us to be certain of our calculations. ► This is very important to Science because we must always show how certain we are in our measurements. ► The greater the number of significant digits, the greater the certainty of measurement. Significant Digits

SIGNIFICANT DIGITS All whole numbers and zeroes between whole numbers are significant. Zeroes at the beginning or the end of a number may or may not be significant. Does the zero have to do with the accuracy of the value? Yes? – SIGNIFICANT Is the zero simply showing how big or small the value is? Called a “placeholder” – NOT SIGNIFICANT ► Examples: ► – 4 sig figs ► 4.03 – 3 sig figs ► 0.04 – 1 sig fig ( leading zeros don’t count) ► – 4 sig figs ► 120 – 2 sig figs ► 120. – 3 sig figs

SIGNIFICANT DIGITS ► Placeholder zeroes has only one significant digit has only one significant digit. ► Any zeros added on the right side ARE significant because they indicate the accuracy of the measurement contains three significant digits contains three significant digits.

PRACTICE Significant Digits ► 1) 1.02 Km = _______ significant Digits ► 2) 0.32 cm = _______ significant Digits ► 3) 3600 kg = _______ significant Digits ► 4) L = ______ significant Digits ► 5) g = ______ significant Digits

ROUNDING NUMBERS ► If the digit after the digit to be rounded is 5 or larger, round up. If not round down. ► Example: ► cm rounded to three Sig. Figs. Digits is 9.15 cm. ► 7.23 g rounded to two Sig. Figs. Digits is 7.2 g.

TRY THESE ROUNDING QUESTIONS ► rounded to one Sig. Fig. Digit ► rounded to three Sig. Fig. Digits ► We now can apply these two concepts to basic mathematical calculations.

Multiplying or Dividing SIGNIFICANT DIGITS ► When multiplying or dividing significant digits, you round to the value with the least total number of sig. figs. ► Example: ► 4.62 x = = 0.16 ► ÷ 6.40 = = 16.8

ADDING OR SUBTRACTING SIGNIFICANT DIGITS ► When adding or subtracting, you round to the value with the least number of Sig. Figs. after the decimal. ► EXAMPLE: ► = = 11.9 ► – 1.07 = = 8.94

PRACTICE ► 1) (2.4)(6.16) = ______ = _____ ► 2) 16.1 – 2.4 = ______ = _____ ► 3) 4.1 ÷ 8.6 = ______ = _____ ► 4) = ____ = _____

ORDER OF OPERATIONS Significant Digits ► You will come across problems involving both x / ÷ and + / -. This is done by using the following rules: 1. Do multiplication/division BEFORE addition/subtractions. 2.Follow the rules of significant digits at each step.

ORDER OF OPERATIONS Significant Digits ► EXAMPLE: 4.3 ÷ = = =9.72=9.7 Division is performed first. This number needs to be rounded to the value with the least total number of sig. digs. This number needs to rounded to the value with the least number of Sig. Digs. after the decimal.

PRACTICE 1) 42 – (2.2)(1.3) 2) (6.2)(4.3) –

Converting Units, Scientific Notation Unit Scientific Notation MassLengthVolume Kilo 10 3 = 1000Kilogram (kg)Kilometre (km)Kilolitre (km) Hecto 10 2 = 100Hectogram (hm) Hectometre (km) Hectolitre (km) Deka 10 1 = 10Decagram (dag) Decametre (dam) Decalitre (dam) Base UnitGram (g)Metre (m)Litre (L) Deci10 -1 = 0.1Decigram (dg)Decimetre (dm) Centi10 -2 = 0.01Centigram (cg)Centimetre (cm) Milli10 -3 = 0.001Milligram (mg)Millimetre (mm) ► You must understand the metric system to effectively convert. Examples: 1 gram (g) = kilogram 1 gram (g) = 100 milligrams Examples: 1 metre (m) = 100 cm 1 metre = kilometres

Scientific Notation ► ► Examples: 1903 x 0.1 = = 1.9 x x = = 2 x Unit conversion 5.1g x 1.2 kg =5.1g x 1200g =6120g =6.1 x 10 3 g

You will also have to use a conversion method that does not involve the metric system or has more than one unit. Example: 1) How many hours is 20.5 minutes? 20.5 min x 1 hour = = h 60 min 60 min 2) How many m/s is 5km/h? 5 km x 1 h x 1000 m = 5000 m= m/s h 3600s 1 km 3600 s h 3600s 1 km 3600 s

► ► P. 349: #6 abcd, #9abcd

REARRANGING FORMULAS ► You must isolate the variable you are trying to solve for. ► To accomplish this you need to use the opposite operation that is indicated. ► EXAMPLE: d = vt ( rearrange for v ) Divide by t because vt is multiplication. d = v t

► There is an easy way to rearrange three part equations using the pie method. ► EXAMPLE: ► This does not work for equations such as: ► a = v f – v i OR c = 2πr ► T D VT v = d / t t = d / v d = vt

PRACTICE ► 1) c = m / v ( rearrange for m ) ► 2) a = ½ bh ( rearrange for h) ► ANSWER: ► 1) m = cv ► 2) h = 2a/b

STEPS FOR SOLVING WORD PROBLEMS 1) List all the known and the unknown from the problem. 2) Select the best formula which uses the known and unknown. (be careful of extraneous info.) 3) Substitute the information into the equation. 4) calculate 5) round with appropriate significant digits. 6) Write a sentence answer.

QUESTIONS ► Text Page 349 ► #1,3,4,6,7,8,9