Significant Figures and Scientific Notation Numbers in Science Significant Figures and Scientific Notation (c) 2013 Vanessa Jason

Measuring in science is very important! Measure Twice, Cut Once. Measuring in science is very important! Doing an experiment is a lot like cooking! It’s important to know the ingredients and the amounts. Working on your car requires specific tools, in exact sizes. A small difference in the concentration or amount of medication a pharmacist gives you may have significant effects on your health. (c) 2013 Vanessa Jason

Why Measure? It is important to obtain measurements because when appropriate calculations are used, experimental results can be compared. (c) 2013 Vanessa Jason

Though measured numbers aren’t exact, they are precise Though measured numbers aren’t exact, they are precise. To be sure that the numbers are as precise as possible, significant figures are used. Example- depending on the precision of your instrument, you could measure water in a graduated cylinder at 2.0, 2.10, or 2.15. The different measurements have a different number of significant figures. (c) 2013 Vanessa Jason

Which numbers are significant? Rule # 1: Every non-zero number is significant Rule #2: Zeros may or may not be significant, depending on their position. And then there are more rules for rule #2… (c) 2013 Vanessa Jason

When are zeros significant? 1. When the 0 is between nonzero digits Examples: 305 has 3 sig figs 4.09 has 3 sig figs 61.02 has 4 sig figs 2. At the end of a number that includes a decimal point Examples: 0.500 has 3 sig figs (5, 0, 0) 25.490 has 5 sig figs (2, 5, 4, 9, 0) 3.00 has 3 sig figs (3, 0, 0) (c) 2013 Vanessa Jason

When are zeros not significant? 1. Before the first nonzero digit Examples: 0.0025 has 2 sig figs (2, 5) 0.0701 has 3 sig fits (7, 0, 1) 2. At the end of a number without a decimal point Examples: 1000 has 1 sig fig (1) 640 has 2 sig figs (6, 4) (c) 2013 Vanessa Jason

Practice: How many sig figs? 2 2.5 inches = _______ sig figs 1.025 feet= _______ sig figs 230.0 meters= _____ sig figs 0.005 miles= ______ sig figs 68.0 grams= ______ sig figs 15.40 liters= _______ sig figs 500,000 ants= _____ sig figs 709 moths= _____ sig figs 4 4 1 3 4 1 3 (c) 2013 Vanessa Jason

Rounding off numbers Sometimes you have a number that must be rounded off to a certain amount of sig figs. Example- 76.493 has 5 sig figs. It needs to be rounded off to 4 sig figs. 76.493= 76.49 What if instead it was 76.499? 76.499= 76.50 (c) 2013 Vanessa Jason

Multiplication and Division In calculations involving multiplication or division, the answer obtained must have the same number of sig figs in the number that has the least amount of sig figs. Example) (190.6)(2.3)= 438.38 Must be rounded in such a way that it contains only two significant figures! Ideas??? 4 sig figs 2 sig figs Cannot have more than 2 sig figs Answer) 440 or 4.4 x 102 (c) 2013 Vanessa Jason

Addition and Subtraction When adding and subtracting numbers, the answer must have the same number of decimal places as the number with the fewest decimal places. (The answer can not be more precise than the least precise measurement). Example- Add 125.17 + 129 + 52.2 125.17 129 52.2 306.37 The number with the least precision is 129. Therefore, the answer must have the same number of decimal places as 129. Answer= 306 (c) 2013 Vanessa Jason

Sig Fig Practice! P.59 in textbook (c) 2013 Vanessa Jason

Scientific Notation That's 200 billion! Some numbers in science are just too big or too small to easily deal with. The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars. That's 200 billion!

How much is a trillion? Somewhere between you 31st and 32nd birthday, you celebrate your 1 billionth second of being born. You would have to live until you were 31,500 years old to celebrate your 1 trillionth second.

If you started at year ONE... and spent a million dollars EVERY DAY, you still would have not spent a trillion dollars. It would take you to the year  2738 to spend a trillion dollars. In short, a trillion, is a LOT.

Scientific Notation How many sig figs does the number 4,500,000,000 have? _____ What about 0.000000000000000915? ____ Very large and very small numbers are often used in science and can be simplified using scientific notation. 2 3 (c) 2013 Vanessa Jason

Scientific Notation Scientific notation is using the power of 10 to write a number. In order to write a number in scientific notation, decimal points must be moved so that it is located after the first nonzero digit. Original decimal point Examples) 4, 500,000,000 Where do we relocate the decimal? .0 After the first nonzero. (c) 2013 Vanessa Jason

Therefore the number 4,500,000,000 would be written as 4.5x109 Scientific Notation Examples) 4, 500,000,000 .0 How many decimal places was the decimal moved? ____ 9 If the decimal is moved to the LEFT, the power of 10 will be a POSITIVE number. If the decimal is moved to the RIGHT, the power of 10 will be a NEGATIVE number Therefore the number 4,500,000,000 would be written as 4.5x109 (c) 2013 Vanessa Jason

Scientific Notation 0.000000000000000915 is a very small number. 10-16 How do we write it in scientific notation? -Move decimal point so that it is located after the first nonzero. -Count how many decimal places it was moved. -To the left= positive exponent; to the right= negative exponent. Answer: 9.15 x ??? 10-16 (c) 2013 Vanessa Jason

Scientific Notation The exponent refers to the number of zeros that follow 1. 1 x 101 = 10 = 10x1 1 x 102 = 100 = 10 x 10 1 x 103 = 1,000 = 10x10x10 1 x 104 = 10,000 = 10x10x10x10 The higher the exponent value, the bigger (or smaller if negative) the number! (c) 2013 Vanessa Jason

Practice Write 5286 in scientific notation. ________ 3 Place the decimal between the 5 and the 2. Since the decimal was moved three places to the left, the power of 10 will be 3. The number 5.286 will be multiplied by 103 =5.286 x 103 Was your answer correct? (c) 2013 Vanessa Jason

More Practice Write 0.000123 in scientific notation: ______________ Write 6,500,000 in scientific notation: ______________ Write 48,000 in scientific notation: (Answer: 1.23 x 10-4) (Answer: 6.5 x 106) (Answer: 4.8 x 104) (c) 2013 Vanessa Jason

Rules for Multiplication in Scientific Notation 1) Multiply the coefficients 2) Add the exponents (base 10 remains) Example 1: (3 x 104)(2x 105) = 6 x 109 What happens if the coefficient is more than 10 when using scientific notation? Example 2: (5 x 10 3) (6x 103) = 30. x 106 While the value is correct it is not correctly written in scientific notation Convert  30.x106 to  3.0 x 107 in scientific notation.

Calculators save time! You need one for this class. Find the sci. notation button on the calculators..... Hint: On most it is an “EXP” or “EE”