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 USING YOUR CALCULATOR, CALCULATE 4.5 X (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.

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 , we write 5.6 x

Examples = 1 x = x = 1 x = x = 1 x = 4.82 x = 1 x = 8.9 x 10 1 (not usually done) 1 = /10 = 0.1 = 1 x = 3.2 x (not usually done) 1/100 = 0.01 = 1 x = 5.3 x /1000 = = 1 x = 7.8 x /10000 = = 1 x = 4.4 x

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.

Practice  Write out the whole number  1.3 X 10 5  1.3 X  Write the following in scientific notation  

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

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

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.

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  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

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 grams grams = grams ≈ grams

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 grams of water x ( grams cisplatin/25.31 grams of water ) = ≈ grams