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Topic 1.2 Units & Measurement What are some examples? Mile, furlong, fathom, yard, feet, inches, Angstroms, nautical miles, cubits There are seven fundamental base units which are clearly defined and on which all other derived units are based: You need to know these This is the unit of distance. It is the distance traveled by light in a vacuum in a time of 1/299792458 seconds. This is the unit of time. A second is the duration of 9192631770 full oscillations of the electromagnetic radiation emitted in a transition between two hyperfine energy levels in the ground state of a caesium-133 atom. This is the unit of electrical current. It is defined as that current which, when flowing in two parallel conductors 1 m apart, produces a force of 2 x 10-7 N on a length of 1 m of the conductors. This is the unit of temperature. It is 1/273.16 of the thermodynamic temperature of the triple point of water. One mole of a substance contains as many molecules as there are atoms in 12 g of carbon-12. This special number of molecules is called Avogadro’s number and equals 6.02 x 1023. This is the unit of mass. It is the mass of a certain quantity of a platinum-iridium alloy kept at the Bureau International des Poids et Mesures in France. THE kilogram! This is the unit of luminous intensity. It is the intensity of a source of frequency 5.40 x 1014 Hz emitting 1/683 W per steradian. The candela is not used in the IB Diploma Program Other physical quantities have units that are combinations of the fundamental units. Speed = distance/time = m.s-1 Acceleration = speed/time = m.s-2 Force = mass x acceleration = kg.m.s-2 (called a newton) (note in IB we write m.s-1 rather than m/s) 1 N = kg.m.s-2 (F = ma) 1 J = kg.m2.s-2 (W = Force x distance) 1 W = kg.m2.s-3 (Power = energy/time) It is sometimes useful to express units that are related to the basic ones by powers of ten See “Data Booklet” from Myclass site 3.3 mA = 3.3 x 10-3 A 545 nm = 545 x 10-9 m = 5.45 x 10-7 m 2.34 MW = 2.34 x 106 W If an equation is correct, the units on one side should equal the units on another. We can use base units to help us check. For example, the period of a pendulum is given by T = 2π l where l is the length in metres g and g is the acceleration due to gravity. In units m = m.s-2 s2 = s How many significant figures are in the following measurements? 425.5 m 0.00043 s 1500 kg 0.006580 A 273.00 K 17.04 m.s-1 Calculate the following with the correct number of sig figs in your answer 13cm + 8.20cm + 0.7051cm 1.500m x 2.01m x 0.5520m Sig figs give an indication of the degree of precision for a measurement and/or a calculation All digits in the measurement are certain, plus the first estimated (uncertain) digit ONLY used when a number is (or is assumed to be) a measured quantity EXACT quantities do not have sig figs i.e.; discrete data For measurements smaller than 1: ◦ 0.004530 For measurements smaller than 1: ◦ 0.004530 Find the first zero on the left-most side For measurements smaller than 1: ◦ 0.004530 From that place onwards, all numbers are significant! For measurements greater than 1: ◦ 45300 For measurements greater than 1: ◦ 45300 Start with the first digit For measurements greater than 1: ◦ 45300 Go right to the last integer, all non zeros are significant For measurements greater than 1: ◦ 45300. Or look for a decimal point, now all numbers are significant Note: we assume that all digits in the textbook are significant eg; 100 kg has 3 s.f. For measurements greater than 1: ◦ 45300 You may see a line instead of a decimal In this case, all numbers up to the line are significant **Remember, sig figs tell the reader the precision in your measurements** How many significant figures are in the following measurements? 425.5 m 0.00043 s 1500 kg 0.006580 A 273.00 K 17.04 m.s-1 4 2 2 (1500. 4) 4 5 4 When adding or subtracting: ◦ Your answer must have the same degree of precision as the least precise measurement ◦ That means your final answer needs to be rounded to the fewest number of decimal places from your measurement When multiplying or dividing: ◦ The number of sig figs in the answer is equal to the least number of sig figs in any of the measurements used in the calculation ◦ NEVER round any numbers until your final answer! Calculate the following with the correct number of sig figs in your answer 13.1cm + 8.202cm + 0.70512cm 22.0cm 1.500m x 2.01m x 0.5520m 1.66m3 Page 6 Questions 15, 16, 18, 19 Reading: Internal Assessment Guide, DCP Part 1