Scientific Notation & Significant Figures. Mergenthaler Vo-Tech HS Mrs. Judith B. Abergos Chemistry 2013

Transcription

1 Scientific Notation & Significant Figures Mergenthaler Vo-Tech HS Mrs. Judith B. Abergos Chemistry 2013

2 Significant Figures Significant Figures digits that show how precise a measurement is The more significant figures you have, the more precise the measurement is 153 is not as precise as cm 153 cm has 3 significant figures cm has 4 significant figures

3 Rules For Significant Figures All non-zero figures are significant (9 sig figs) Zeros trapped between other sig figs are significant 401 (3 sig figs) 306, 30.6, 3.06 and.306 (3 figs) Zeros after a decimal are significant 4.00 (3 sig figs) 279.0, and (4 figs) Leading zeros and trailing zeros are NOT significant 400 (1 sig fig) (3 sig fig)

4 Additional Rules Note that for multiplication and division, significant figures are counted. For addition and subtraction, the decimal places are counted.

5 For addition and subtraction the result has the same number of decimal places as the least precise measurement used in the calculation. Example: (too many sig figs!) Choose 4 significant figures, because the second number has only one place to the right of the decimal point.

6 For multiplication and division the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. Example: 18.1 x = Use correct number of sig. figs.: 2.39 * 10^3 In this example the number 18.1 determines the significant figures.

7 Scientific Notation

8 Chemistry deals with very large and very small numbers. Consider this calculation: ( x 30,000,000,000) Hopefully you can see, how awkward it is keeping track of all those zeros!

9 Scientific Notation a shorter way to write extremely big or extremely small numbers General Format: N x 10 x 6.63 x x / x 10-8 It is now much more compact, it better represents significant figures, and it is easier to manipulate mathematically. ( x 30,000,000,000)

10 Scientific Notation Rules Used to represent positive numbers only. Standard position for the decimal point is just to the right of the first non-zero digit in the number. Will always produce a number between 1 and x 10 7 is not in correct scientific notation x 10 6

11 Helpful Hint The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

12 Standard Scientific Notation Really Big Number: 3,780,000,000,000, Place the decimal to the right of the first non-zero digit (drop ending 0 s) Add the x 10 part x Count how many places you had to move the decimal to do step 1. This number is going to be your exponent. If you had to move the decimal to the left the exponent is positive, to the right the exponent is negative x 10 15

13 Standard Scientific Notation Really Small Number: Place the decimal to the right of the first non-zero digit (drop ending 0 s) Add the x 10 part x Count how many places you had to move the decimal to do step 1. This number is going to be your exponent. If you had to move the decimal to the left the exponent is positive, to the right the exponent is negative x 10-10

14 Scientific Notation Standard Scientific Notation Number: x 10 8 Move the decimal the same number of places as the exponent. Positive exponent: move right Negative exponent: move left 260,500,000 Another Example Scientific Notation Number: x

15 Write the number in standard notation. A = 100, , ,000 Think: Move the decimal right 5 places.

16 Write the number in standard notation. B = 1000 Divide by the reciprocal. Think: Move the decimal left 3 places.

17 Write the number in standard notation. A = 1,000,000, ,000,000,000 2,870,000,000 Think: Move the decimal right 9 places.

18 Write in scientific notation Move the decimal to get a number 7.09 between 1 and Set up scientific notation. Think: The decimal needs to move left to change 7.09 to , so the exponent will be negative. Think: The decimal needs to move 3 places. So written in scientific notation is Check = =

19 Write in scientific notation Move the decimal to get a number 8.11 between 1 and Set up scientific notation. Think: The decimal needs to move left to change 8.11 to , so the exponent will be negative. Think: The decimal needs to move 4 places. So written in scientific notation is Check = =

20 Convert x 10 9 to scientific notation