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Significant Figures & Measurements. How good is good enough?. Significant Figures. The digits in a measured number that indicate the measuring equipments degree of precision This means: The numbers that show how careful you were with the measurements. 4.25 cm.
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Significant Figures & Measurements How good is good enough?
Significant Figures The digits in a measured number that indicate the measuring equipments degree of precision • This means: The numbers that show how careful you were with the measurements. 4.25 cm There are three significant figures here.
Significant Figures • Generally, you should write all of the digits that you obtained directly with the measuring device and add a final digit that you’ve estimated. • For example, if you have a ruler that can measure length in millimeters, you should write the lengths of objects you’ve measured to tenths of millimeters.
Sig Fig Rules How do I know what numbers are significant?
Sig Fig Rules So, let’s see what that means: 1 0.02 grams has _________ sig figs 3 501 mL has _________ sig figs 4 0.1020 Km has _________ sig figs 6 6,051.00 grams has _________ sig figs 2 33,000 mm has _________ sig figs
Scientific Notation Scientific notation is a way to write very large or very small numbers. • The decimal point is moved so that there is one digit in the unit’s position and all of the decimal places are held as a power of ten. • This is important in chemistry because many of the measurements we make either involve very large numbers of atoms/molecules or very tiny measurements, such as masses of electrons or protons. • For example, consider 839, 000, 000. While this number is not too difficult to write out, it is more conveniently written in scientific notation. • Written in scientific notation, this number becomes: 8.39×108. • The “108” means that ten is multiplied by itself eight times: 10×10×10×10×10×10×10×10. • As you can see, writing 108 is much easier!
Scientific Notation Let’s practice with the following numbers: 47,500 = 3.825 x 103 = 0.00067 = 0.2713 = 4.44 x 10-3 4.75 x 104 3,825 6.7 x 10-4 2.713 x 10-1 0.00444 3 sig figs 4 sig figs 2 sig figs 4 sig figs 3 sig figs
Sig Figs and Math Why don’t math classes worry about Sig Figs? • Because math doesn’t worry about UNITS, they don’t worry as much about sig figs! • Science DOES!.
Adding & Subtracting 334.540 grams + 198.9916 grams = 533.532 g (rounded from 533.5316 g) 3 places after the d.p. 4 places after the d.p. -0.12 m(rounded from -0.119 m) 0.0610 m – 0.18 m = 4 places after the d.p. 2 places after the d.p. 450. cm (rounded from 450.1 cm) 349.0 cm + 1.10 cm + 100. cm = 1 place after d.p. 2 places after d.p. 0 places after d.p.
Multiplying or dividing 3.4 g/mL (rounded from 3.366 g/mL) 34 grams ∕ 10.1 mL = 2 s.f. 3 s.f. 2.61 x 106 joules / 0.0034 seconds = 7.7 x 108 J/s (rounded from 7.676470588 x 108 J/s 3 s.f. 2 s.f. 900 m (rounded from 880 m) 44 m/s x 20 s = 2 s.f. 1 s.f.
