Scientific Notation Find your Notecard Partner Why would

Scientific Notation Find your Notecard Partner. Why would we use scientific notation?

What is the Length? We can see the markings between 1. 6 -1. 7 cm 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 2

Learning Check What is the length of the wooden stick? 1) 4. 5 cm 2) 4. 58 cm 3) 4. 584 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, 10 m. L<V<20 m. L The 1’s digit is also certain, 17 m. L<V<18 m. L A best guess is needed for the tenths place. Chapter Two 4

SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY OR REALLY, REALLY SMALL BIG 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?

Change to standard form. 1. 87 x 10– 5 = 0. 0000187 3. 7 x 108 = 370, 000 7. 88 x 101 = 78. 8 2. 164 x 10– 2 = 0. 02164

Change to scientific notation. 12, 340 = 1. 234 x 104 0. 369 = 3. 69 x 10– 1 0. 008 = 8 x 10– 3 3 1. 000 x 10 1, 000. =

NEED TO KNOW Prefixes in the SI System Power of 10 for Prefix Symbol Meaning Scientific Notation _____________________________ mega- M 1, 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. 00001 10 -9 pico- p 0. 0000001 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

Significant figures The number of significant digits is independent of the decimal point. These numbers All have three significant figures! 255 31. 7 5. 60 0. 934 0. 0150

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. 0. 421 - three ? ? ? significant figures Leading zero Captive zeros are always significant! Captive zeros 4, 008 - ? ? ? four significant figures 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 __ 3 significant figures 0. 00230 kg __ 3 significant figures 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? speed = 1. 0 km 3. 0 min = 0. 33 km min 0. 333333

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 cm 2 135 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 1 st insignificant digit 34. 204221 becomes 34. 20

Examples of Rounding For example you want a 4 Sig Fig number 0 is dropped, it is <5 4965. 03 4965 780, 582 780, 600 8 is dropped, it is >5; Note you must include the 0’s 1999. 5 2000. 5 is dropped it is = 5; note you need a 4 Sig Fig

Multiplication and division 32. 27 1. 54 = 49. 6958 49. 7 3. 68 . 07925 = 46. 4353312 46. 4 1. 750 . 0342000 = 0. 05985 3. 2650 106 4. 858 = 1. 586137 107 1. 586 107 6. 022 1023 1. 661 10 -24 = 1. 000000 1. 000