Scientific Notation and Converting Units Chemistry I

Bell Work Which do you feel is “easier” to read? Easier to write? 1.7 x 1018 1,700,000,000,000,000,000 Why do you think that?

SI measurement Le Système international d'unités The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly Metrication is a process that does not happen all at once, but is rather a process that happens over time. Among countries with non-metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1866. Information from U.S. Metric Association

Chemistry In Action On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat. 1 lb = 1 N 1 lb = 4.45 N “This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the standard for length was the king’s foot. What are some problems with this standard?

What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. For very large and very small numbers, scientific notation is more concise.

Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10x

To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Examples Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108 Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4

To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

Example Given: 5.093 x 106 Answer: 5,093,000 (moved 6 places to the right) Given: 1.976 x 10-4 Answer: 0.0001976 (moved 4 places to the left)

Learning Check Express these numbers in Scientific Notation: 405789 0.003872 3000000000 2 0.478260

Scientific Notation Two main reasons: 1. scientists are too lazy to write the whole number out (and too many zeros to count!!) 2. easier to read

What is Scientific Notation? Ex: 1.9 x 105 A number in scientific notation has two parts 1. A number between 1 and 10 (not including 10) 2. A power of ten It says you must multiply 1.9 x 10 five times to get the number - 190000

How do I write scientific notation? Ex: 7,200 1. Write any non-zero numbers down in decimal form so they are less than 10 Ex: 7,200  7.2 Tack on “x 10” 7.2 x 10 3. Count how many times the decimal point must be moved to bring it to its final position – this is the exponent (negative sign if a number smaller than zero) 7.2 x 103

Practice! 8,900,000 8.9 x 106 0.0000873 8.73 x 10-5 470,000,000 4.7 x 108 0.000018 1.8 x 10-5

Converting Scientific Notation to a Number Ex: 4.7 x 10-3 1. Write the non-zero numbers with the decimal 4.7 2. Move the decimal place the direction and the number of places the exponent tells you 0.0047

Practice! 2.9 x 108 290000000 5.6 x 10-4 0.00056 3.1 x 102 310 5.67 x 10-6 0.00000567