Find your Notecard Partner. Why would we use scientific notation?
What is the Length? We can see the markings between 1.6-1.7cm We can’t see the markings between the .6-.7 We must guess between .6 & .7 We record 1.67 cm as our measurement The last digit an 7 was our guess...stop there
Learning Check What is the length of the wooden stick? 1) 4.5 cm
Measurement and Significant Figures Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10’s place, 10mL<V<20mL The 1’s digit is also certain, 17mL<V<18mL A best guess is needed for the tenths place. Chapter Two
REALLY, REALLY SMALL NUMBERS. SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.
Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 105 is not in proper scientific notation. Why?
0.0000187 370,000,000 78.8 0.02164 Change to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 0.0000187 370,000,000 78.8 0.02164
Change to scientific notation. 12,340 = 0.369 = 0.008 = 1,000. = 1.234 x 104 3.69 x 10–1 8 x 10–3 1.000 x 103
NEED TO KNOW Prefixes in the SI System Power of 10 for Prefix Symbol Meaning Scientific Notation _________________________________________________________ mega- M 1,000,000 106 kilo- k 1,000 103 deci- d 0.1 10-1 centi- c 0.01 10-2 milli- m 0.001 10-3 micro- m 0.000001 10-6 nano- n 0.000000001 10-9 pico- p 0.000000000001 10-12
Significant figures ??? Method used to express accuracy and precision. You can’t report numbers better than the method used to measure them. 67.20 cm = four significant figures ??? Certain Digits Uncertain Digit
The number of significant digits is independent of the decimal point. Significant figures The number of significant digits is independent of the decimal point. 255 31.7 5.60 0.934 0.0150 These numbers All have three significant figures!
Rules for Counting Significant figures Every non-zero digit is ALWAYS significant! Zeros are what will give you a headache! They are used/misused all of the time. SEE p.24 in your book!
Rules for zeros Leading zeros are not significant. ??? Captive zeros are always significant! 0.421 - three significant figures Leading zero ??? 4,008 - four significant figures Captive zeros ??? Trailing zeros are significant … IF there’s a decimal point in the number! 114.20 - five significant figures Trailing zero ???
Examples 250 mg \__ 2 significant figures 120. miles 0.00230 kg 23,600.01 s \__ 7 significant figures
Significant figures: Rules for zeros Scientific notation - can be used to clearly express significant figures. A properly written number in scientific notation always has the proper number of significant figures. 0.00321 = 3.21 x 10-3 Three Significant Figures
Significant figures and calculations An answer can’t have more significant figures than the quantities used to produce it. Example How fast did you run if you went 1.0 km in 3.0 minutes? 0.333333 speed = 1.0 km 3.0 min = 0.33 km min
Significant figures and calculations Multiplication and division. Your answer should have the same number of sig figs as the original number with the smallest number of significant figures. ONLY 3 SIG FIGS! 21.4 cm x 3.095768 cm = 66.2 cm2 135 km ÷ 2.0 hr = 68 km/hr ONLY 2 SIG FIGS!
Significant figures and calculations Addition and subtraction Your answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with. 123.45987 g + 234.11 g 357.57 g 805.4 g - 721.67912 g 83.7 g
Rounding off numbers After calculations, you may need to round off. If the first insignificant digit is 5 or more, you round up If the first insignificant digit is 4 or less, you round down.
Examples of rounding off If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then - 2.5795035 becomes 2.580 34.204221 becomes 34.20 1st insignificant digit
Examples of Rounding For example you want a 4 Sig Fig number 0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965.03 780,582 1999.5 4965 780,600 2000.
Multiplication and division 32.27 1.54 = 49.6958 3.68 .07925 = 46.4353312 1.750 .0342000 = 0.05985 3.2650106 4.858 = 1.586137 107 6.0221023 1.66110-24 = 1.000000 49.7 46.4 .05985 1.586 107 1.000