Objective The student will be able to: express numbers in scientific and decimal notation.

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer

Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

Write 28750.9 in scientific notation. 2.87509 x 10-5 2.87509 x 10-4 2.87509 x 104 2.87509 x 105

2) Express 1.8 x 10-4 in decimal notation. 0.00018 3) Express 4.58 x 106 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button. 4.58 x 106 is typed 4.58 6

Write in PROPER scientific notation Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) 234.6 x 109 2.346 x 1011 9) 0.0642 x 104 on calculator: 642 6.42 x 10 2

Write 531.42 x 105 in scientific notation.

Scientific Notation Quick Review

Powers of 10 http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/ http://www.powersof10.com/ Powers of 10 - Google Videos

Question 1 Write 4,776 in scientific notation Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between one and ten. 4.776 Count the number of digits between the old and the new decimal point, this gives the power, n of 10 (10n). 4 776 3 Digits X 103 Since the decimal is shifted to the left, the exponent is positive. 4.776 x 103

Question 6 Write 0.0246 in scientific notation Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between one and ten 2.46 Count the number of digits between the old and the new decimal point, this gives the power, n of 10 (10n). 0 02 46 2 Digits X 10-2 Since the decimal is shifted to the right, the exponent is negative. 2.46 x 10-2

Write the decimal number. Question 14 Write 4.953 x 104 in standard form Write the decimal number. 4.953 Move the decimal the number of places specified by the powers of ten: to the right since it is positive. 4 9530 X 104 4 Places Rewrite the number in integer/standard form. 49,530

Write the decimal number. Question 17 Write 8.397 x 10-1 in standard form Write the decimal number. 8.397 Move the decimal the number of places specified by the powers of ten: to the left since it is negative. 0 8 397 X 10-1 1 Place Rewrite the number in integer/standard form. 0.8397

Multiplying and Dividing With Your Calculator Punch the number (the digit number) into your calculator. Push the EE or EXP button. Do NOT use the x (times) button!! Enter the exponent number. Use the +/- button to change its sign. Voila! Treat this number normally in all subsequent calculations. Scientific Calculator Scientific calculator for chemists with notebook http://www.calculator.com/calcs/calc_sci.html

Scientific Notation Tutorials http://www.wwnorton.com/college/chemistry/gilbert/tutorials/ch1.htm (Click on Scientific Notation Link - view tutorial) http://www.visionlearning.com/library/module_viewer.php?mid=47&l=&c3 (Read Scientific Notation towards the bottom of the page) http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut3_scinot.htm