SCIENTIFIC NOTATION Scientific Notation Some scientific measurements can

SCIENTIFIC NOTATION

Scientific Notation � Some scientific measurements can result in very large or very small numbers � These numbers can be converted into SCIENTIFIC NOTATION to express them in a more concise form. � EX = 1. 496 x 108 km

Why use scientific notation? To express very large or very small numbers in a more concise form. � Numbers expressed in scientific notation are easier to use in calculations. �

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

Writing Scientific Notation � In the original number (149, 600, 000), place the decimal point so that there is one nonzero digit to the LEFT of the decimal point. N = 1. 49600000 � Count the number of places that the decimal point “moved” – this will be the exponent x=8 1. 496 x 108 km

Scientific Notation of Small Numbers � In small numbers, the decimal place will be moved to the RIGHT 0. 000567 N = 5. 67 � The exponent will then be NEGATIVE: 5. 67 X 10 -4

Your Turn � Express 289, 800, 000 in proper scientific notation �Which way will you move the decimal? �How many places will you move the decimal?

Answer You would move the decimal 8 places to the left � Answer: 2. 898 x 108 �

Your Turn � Express 0. 000567 in proper scientific notation �Which way will you move the decimal? �How many places will you move the decimal?

Answer � You would move the decimal 4 places to the right � 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. 4. 56 x 104 = 45, 600 � Move the decimal point to the left for negative exponent 10. 4. 56 x 10 -4 = 0. 000456 (Use zeros to fill in places. )

Your Turn � Express 5. 093 x 106 in standard form �Which way will you move the decimal? �How many places will you move the decimal?

Answer � You would move the decimal 6 places to the right � Answer: 5, 093, 000

Your Turn � Express 1. 976 x 10 -4 in standard form �Which way will you move the decimal? �How many places will you move the decimal?

Answer � You would move the decimal 4 places to the left � Answer: 0. 0001976

Scientific notation in unit conversions � Scientists also use scientific notation when performing unit conversions

Your Turn � Express 0. 004 mm in meters and scientific notation �Which way will you move the decimal? �How many places will you move the decimal? ○ Hint: first put the number in correct scientific notation then add the conversion power ○ mm = 10 -3 m

Answer � You would move the decimal 6 places to the left � Answer: 4. 0 x 10 -6 m

Your Turn � Express 5. 3 mm in meters and scientific notation �Which way will you move the decimal? �How many places will you move the decimal? ○ Hint: mm = 10 -3 m

Answer � You would move the decimal 3 places to the left � Answer: 5. 3 x 10 -3 m