ACCURACY, PRECISION and SIGNIFICANT FIGURES



SIGNIFICANT FIGURES & SCIENTIFIC NOTATIONLEARNING GOAL: I will be able to determine the number of significant figures, convert between scientific notation and ordinary notation, and express calculated problems using sig figs.1. SIGNIFICANT FIGURESThe precision of a measurement is expressed in terms of significant figures (SF). The value 5.2 has 2 SF while 5.20 has 3 SF. The extra zero at the end makes this measurement more precise and is included as a SF. A zero before the first digit does not count as significant, as precision is not increased. State the number of SF in each of the following a) 0.0420 kmb) 4.1 g c) 3.9120 m d) 0.031 mL e) 0.310 gf) 0.00310 mgg) 0.037 km h) 3.037 km 2. SCIENTIFIC NOTATIONScientific notation is used to control the number of significant digits in both large & small numbers. The rule here is simple… ignore the exponent! 3.4 x 103 has 2 SF; so does 3.4 x 10-5 & 3.4 x 108. EX: 2000 km could have 1 SF, or 2, or 3, or 4; but 2 x 103 km is unambiguously expressed to 1 SF while 2.00 x 103 km is more precisely expressed with 3 SF.State the number of SF in each of the following a) 4.52 x 104 =b) 5.915 x 10–7 =c) 2 x 10–3 =d) 3.001 x 10–5 =Convert the following measurements from SN a) 4 x 104 = b) 4.0 x 10–4= c) 3.2 x103 = d) 3.200x103 =3. WORKING WITH SIGNIFICANT FIGURESThere are 2 rules you should remember i) The result of a calculation cannot be expressed to a greater number of SF than the least precise of the measurements or estimates.ii) The working in a calculation should be expressed to at least 1 more SF than the result will be. Don’t round off until the end.Ex 1: A car travels 625.4 km in 8.2 h. Calculate its velocity.Velocity = distance / time= 625.4/8.2 km/h * 8.2 h is the least precise measurement 2 SF= 76.3 km/h = 76 km/h *the answer can have no more than 2 SF of precisiona) A teacher gives 66.0 g of candy to each of her 28 students. How much candy does she give out? **Note: 28 is a counted number…b) A 694 kg concrete slab is 1.47 m long, 1.2 m wide & 0.500 m high. Calculate its density (mass/volume). ................
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