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Chapter 2 Introduction Additional Resources SCIENTIFIC MEASUREMENT AND DIMENSIONAL ANALYSIS Chapter 2 Memorise Understand Importance * SI units and prefixes * Dimensional analysis High level: 11% of GAMSAT Section 3 maths-based questions released by ACER are related to content in this chapter (in our estimation). * Note that approximately 90% of such questions are related to just 3 chapters: 1, 2, and 3. Introduction It is extremely important to know the SI system of measurement for the GAMSAT. The metric system is very much related to the SI system. The British system, though familiar, does not need to be memorised for the GAMSAT (related questions would only be asked if relevant conversion factors were provided). 'Dimensional analysis' is a technique whereby simply paying attention to units and applying the basic algebra we covered in GM Chapter 1, you will be able to solve several real exam questions in GAMSAT Physics, Chemistry and Biology – even without previous knowledge in those subjects. Additional Resources Open Discussion Boards Special Guest GAMSAT MATHS GM-37 2.0 Yes, GAMSAT Has a Need for Speed! A ‘unit’ is any standard used for Physics easier. It is normal if you cannot fill making comparisons in measurements. out the tables now, but please return to this Units form an important part of the founda- page after you have studied this chapter so tion of science and GAMSAT Section 3. you can complete all entries below. For non-science students, this is a Science students? Do your best, be new language to learn but the vocabulary quick, note that some entries that appear is incredibly small. The units below can all simple may surprise you! ACER has exam be found in this chapter, and throughout questions directly dependent on your GAMSAT Physics and Chemistry. Your famil- understanding of SI units and prefixes, so High-level Importance iarity with these units will make your study of let’s get started… Section Units 2.1.3 length: electric current: Table 1: SI Base mass: thermodynamic temperature: Units time: amount of substance: Section Units 2.1.3 area: speed, velocity: Table 2: Examples volume: acceleration: of SI Derived Units Section Units 2.1.3 frequency: power: Table 3: SI electric charge, quantity force: of electricity: Derived Units with Special Names electric potential difference, pressure, stress: electromotive force: and Symbols energy, work, quantity of heat: Section Base 10 tera: deci: 2.1.3 giga: centi: Table 4: Important mega: milli: SI prefixes for GAMSAT, A closer kilo: micro: look hecto: nano: deca: pico: GM-38 Chapter 2: SCIENTIFIC MEASUREMENT AND DIMENSIONAL ANALYSIS GAMSAT MASTERS SERIES 2.1 Systems of Measurement High-level Importance 2.1.1 British Units (Imperial System of Measurement) You are probably already familiar with Minutes There are 60 seconds in several of these units of measurement, but we every minute. 1 min. = 60 s. recommend reviewing them at least once. Hours There are 60 minutes in every A. Length: These units are used to hour. 1 h. = 60 min. describe things like the length of physi- cal objects, the displacement of a physical Days There are 24 hours in every object, the distance something has traveled day. 1 day = 24 h. or will travel, etc. Area and volume are also measured as the square and cube (respec- Years The year is the largest unit tively) of these units. of time in the British System. There are 365 days in every Inches The inch is the smallest year. 1 yr. = 365 days measurement of length in the British System. C. Mass/Weight: These terms are not Feet There are 12 inches in every technically the same and we will discuss the foot. 1 ft. = 12 in. differences in Physics. The following units describe the amount of matter in an object. Yards There are 3 feet in every yard. 1 yd. = 3 ft. Ounces The ounce is the smallest unit of mass in the British System. Miles The mile is the largest unit of length in the British System. Pounds There are 16 ounces (oz.) in There are 5,280 feet in every every pound (lb.). 1 lb. = 16 oz. mile. 1 mi. = 5,280 ft. Tons The ton is the largest unit of mass in the British System. B. Time: These units describe the passage There are 2,000 lbs. in an of time. American ton, and 2,240 lbs. in a British tonne. Neither Seconds The second is the smallest unit should be committed to of time in the British System. memory. GAMSAT MATHS GM-39 2.1.2 Metric Units Measuring with Powers of 10: Unlike As you go down, you divide by 10 and the British System, the Metric System has as you go up, you multiply by 10 in order to only one unit for each category of measure- convert between the units. ment. In order to describe quantities that are much larger or much smaller than one EXAMPLE of the base units, a prefix is chosen from a How many metres is 1 kilometre? variety of options and added to the front of High-level Importance the unit. This changes the value of the unit 1 km = 1000 m by some power of 10, which is determined by what the prefix is. The following are the From general knowledge, we know most common of these prefixes (with the that kilo means one thousand. This means representative symbols in brackets): there are 1000 metres in a kilometre. But just in case you get confused, you can also - use the clue from the mnemonic. Now we Milli (m) One thousandth (10 3) of the know that Kilo is three slots upward from base unit the Unit base. Hence we multiply 3 times by - 10: 10 × 10 × 10 = 1000. Centi (c) One hundredth (10 2) of the base unit An even less confusing way to figure out how to do the metric conversions quickly and One tenth (10-1) of the base Deci (d) accurately, is to use a metric conversion line. unit This is quite handy with any of the common units such as the metre, litre, and grams. Deca (da) Ten (101) times the base unit Kilo (k) One thousand (103) times the K H D U D C M base unit There is a mnemonic that may be m l used to identify these prefixes: g King Kilometre Kilo Henry Hectometre Hecto (h) Figure GM 2.1: The Metric Conversion Died Decametre Deca Line. The letters on top of the metric line Unexpectedly Unit Base Unit stands for the “King Henry” mnemonic. On Drinking Decimetre Deci the other hand, the letters below the metric line - m, l, g – stand for the unit bases, metre, Chocolate Centimetre Centi litre, or gram, respectively. Milk Milimetre Milli GM-40 Chapter 2: SCIENTIFIC MEASUREMENT AND DIMENSIONAL ANALYSIS GAMSAT MASTERS SERIES To use this device, draw out the Now, let’s try converting centimetre to metric line as shown in Fig GM 2.1. From kilometre: What is 6.3 cm in km? the centremost point U, the prefixes going High-level Importance to the left represent those that are larger 1. Place your pen on the c (centi) point than the base unit (kilo, hecto). These also in the metric line. correspond to the decimal places that you will be moving from the numerical value of 2. Moving from c to k (kilo) takes five the unit to be converted. Those going to places going to the left. This also the right are for the ones smaller than the means moving five places from the unit (deci, centi, milli). decimal point of the number 6.3. 6.3 cm = .000063 km EXAMPLE Using this method definitely makes doing the metric conversions so much How much is 36 litres in millilitres? faster than the fraction method! Step 1: Place your pen on the given unit, in this case L (litre). Then count the There are other prefixes that are often number of places it takes you to reach the used scientifically: unit being asked in the problem (millilitre). Tera (T) 1012 times the base unit Giga (G) 109 times the base unit 6 k h d u d c m Mega (M) 10 times the base unit Micro (μ) 10-6 of the base unit Nano (n) 10-9 of the base unit Pico (p) 10-12 of the base unit L A. Length: As with British length units, : Converting litre to millilitre Fig GM 2.2 these are used to measure anything that has using the metric conversion line. to do with length, displacement, distance, etc. Area and volume are also measured as the Step 2: Because it took you three places square and cube (respectively) of these units. going to the right to move from the litre to the millilitre units, you also need to add Metres The metre is the basic unit of three places from the decimal point of the length in the Metric System. number 36.0. Other millimetre, centimetre, 36 L = 36,000 ml Common kilometre Forms GAMSAT MATHS GM-41 B. Time: These are units that quantify the C. Mass: These are units that describe passage of time. the amount of matter in an object. Seconds Just as in the British System, Grams The gram is the basic metric the second is the basic unit unit of mass. of time in the Metric System. Minutes, hours, and the other Other milligram, kilogram British units are not technically Common part of the Metric System, but Forms they are often used anyway in High-level Importance problems involving metric units. Other millisecond Common Forms 2.1.3 SI Units SI units is the International System of Units (abbreviated SI from the French NOTE Le Système International d'Unités) and is a modern form of the metric system.
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