1. Aim: How to write in Scientific Notation and Count Significant Figures DO NOW: 1. WHAT DOES 10 5 MEAN? 2. WHAT IS THE VALUE OF 10 5. 3. USING YOUR CALCULATOR, CALCULATE 4.5 X 10 6. (INPUT AS 4.5 X 10^6) 4. WOULD IT EASIER TO WRITE THE WHOLE VALUE OR JUST AS 4.5 X 10 6 EXPLAIN.

2. Scientific Notation  In scientific notation, a given number is written as the product of two numbers; a coefficient and 10 raised to a power.  Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10 - 9

3. Examples 10000 = 1 x 10 4 24327 = 2.4327 x 10 4 1000 = 1 x 10 3 7354 = 7.354 x 10 3 100 = 1 x 10 2 482 = 4.82 x 10 2 10 = 1 x 10 1 89 = 8.9 x 10 1 (not usually done) 1 = 10 0 1/10 = 0.1 = 1 x 10 - 1 0.32 = 3.2 x 10 - 1 (not usually done) 1/100 = 0.01 = 1 x 10 - 2 0.053 = 5.3 x 10 - 2 1/1000 = 0.001 = 1 x 10 - 3 0.0078 = 7.8 x 10 - 3 1/10000 = 0.0001 = 1 x 10 - 4 0.00044 = 4.4 x 10 - 4

4. Writing in Scientific Notation  As you can see, the exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left.

5. Practice  Write out the whole number  1.3 X 10 5  1.3 X 10 -5  Write the following in scientific notation  0.0000456  13 450 000 000 000 000

6. Scientific Notation and Your Calculator  How to input scientific notation on your scientific calculator:  Us the ^ button before exponent  ( 3.7 x 10 ^ 3)  When doing calculations with scientific notation, put your numbers in scientific notation in parenthesis  (2.3 x 10 4 ) – (3.7 x 10 3 )  If a number like this shows up your calculator : 1.89E5 it is the same as 1.89 x 10 5

7. Your Turn (On your Own)  Question 1Write in scientific notation: 0.000467 and 32000000  Question 2Express 5.43 x 10 -3 as a number not in scientific notation.  Question 3(4.5 x 10 -14 ) x (5.2 x 10 3 ) = ?  Question 4(6.1 x 10 5 )/(1.2 x 10 -3 ) = ?

8. Significant Figures  Significant figures refers the digits in a measured number (or in the result of a calculation with measured numbers) that include all certain digits plus a final digit having some uncertainty.

9. Rules to Significant Figures  All non-zero digits (1, 2, 3, 4, etc.) are significant.  Zeroes between non-zero digits are significant. Ex: 101  Zeroes to the left of the first non-zero digit are not significant. Ex 0.0000101  Zeroes to the right of the last non-zero digit are significant if there is a decimal point present, but not significant if there is no decimal point.  Significant: 100. has three significant figures  Not significant: 100 has one significant figure

10. Significant Figures in Calculations  For addition and subtraction problems, the answer should be rounded off to the same number of decimal places as the measurement with the fewest decimal places. 184.2 grams+ 2.324 grams = 186.524 grams ≈ 186.5 grams

11. Significant Figures in Calculations  For multiplication and division problems, round off the answer to the same number of significant figures in the measurement with the fewest significant figures. 100.0 grams of water x (0.0634 grams cisplatin/25.31 grams of water ) = 0.250493875 ≈ 0.250 grams