Scientific Notation

The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier. Examples: The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms. Scientists can work with very large and very small numbers more more easily if the numbers are written in scientific notation.

Objective The student will be able to: express numbers in scientific and decimal notation. Designed by Skip Tyler, Varina High School

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

Rules to Remember! If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. positive left

Rules to Remember! If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. negative right

1. Move the decimal to the right of the first non-zero number. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive.

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

Write 531.42 x 105 in scientific notation.

Practice Problems ANSWERS PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2 Put these numbers in scientific notation. PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2 1.2 x 101 9.87 x 10-1 5.96 x 102 7.0 x 10-7 1.0 x 106 1.26 x 10-3 9.88 x 1011 8 x 100 ANSWERS .00012 1000 0.01 12 .987 596 .000 000 7 1,000,000 .001257 987,653,000,000 8

EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMS ANSWERS 4.9 X 102 3.75 X 10-2 5.95 X 10-4 9.46 X 103 3.87 X 101 7.10 X 100 8.2 X 10-5 490 .0375 .000595 9460 38.7 7.10 .000082

Brain Break

Using the Exponent Key on a Calculator

EE or EXP means “times 10 to the…” How to type out 6.02 x 1023: How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2 Don’t do it like this… WRONG! 6 y x . 3 2 WRONG! …or like this… x 1 6 . 2 EE 3 …or like this: TOO MUCH WORK. y x 3 2 x 1 6 .

How to Use a Scientific Calculator Divide: (5.44 x 107) (8.1 x 104) . 671.604938 54400000. 5.44 8.1 00 07 00 04 How to enter this on a calculator: . 5.44 7 8.1 4 EE . EE ENTER OR . 5.44 7 8.1 4 EXP . EXP = 671.6049383 rounded to 6.7 x 102 Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52

Example: 1.2 x 105 2.8 x 1013 = 1 . 2 EE 5 3 8 Type this calculation in like this: 4.2857143 –09 Calculator gives… 4.2857143 E–09 or… This is NOT written… 4.3–9 4.3 x 10–9 4.3 E –9 or But instead is written…

= -6.525 x 10-9 report -6.5 x 10-9 (2 sig. figs.) = 5.3505 x 103 or 5350.5 report 5.35 x 103 (3 sig. figs.) = 5.84178499 x 10-13 report 5.84 x 10-13 (3 sig. figs.) = 2.904 x 1023 report 2.9 x 1023 (2 sig. figs.) = -3.07122 x 1016 report -3.1 x 1016 (2 sig. figs.)