BY: CLAUDIA HYSA & DOUG STRICKLE SCIENTIFIC NOTATIONS

HISTORY Archimedes was a Greek inventor and mathematician who studied at the Egyptian city of Alexandria. He would preform different problems in Greek numerals, obviously because the modern number system had not been invented yet. Archimedes basically discovered that you can make very small numbers into very small numbers by what is now called Scientific Notation.

HOW TO CONVERT TO A SCIENTIFIC NOTATION (POSITIVE NUMBERS) Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number and a power of ten. This number is always one more and one less than ten. A number can be converted to scientific notation by increasing the power of ten by one for each place the decimal point is moved. Example: 1.2 x 10 9 = 1,200,000,000

HOW TO CONVERT TO A SCIENTIFIC NOTATION (NEGATIVE NUMBERS) To make it negative you move the decimal to the right (To make it positive, you move it to the left.) If you have a number smaller than one in absolute value, it is considered a negative. -Warning! A negative on an exponent is totally different than a negative on a number! For example: – = –3.6 × 10 – = 3.6 × 10 –4 36,000 = 3.6 × 10 4 –36,000 = –3.6 × 10 4

HOW TO CONVERT A SCIENTIFIC NOTATION TO STANDARD FORM (POSITIVE) Move the decimal point to the right for positive exponents of ten. The exponent tells you how many places to move. Move the decimal point to the left for negative exponents of ten. Again, the exponent tells you how many places to move. Example: 1,200,000,000 = 1.2x10 9

HOW TO CONVERT A SCIENTIFIC NOTATION TO STANDARD FORM (NEGATIVE) Basically, all you do is move the decimal to the left until it becomes a positive number, or a whole number. Converting the number back to a decimal is easy! All you do is move the decimal how ever many places the exponent is telling you to. Example: 6.5 x =

REAL WORLD EXAMPLES 7 x10 9 = Population of the world is around 7 billion written out as 7,000,000, x10 14 = Approximate number of cells in the human body is 100 trillion or 100,000,000,000, x10 7 = Distance from the Earth to the sun is 93 million miles or 93,000,000 miles 1.4 x10 8 = Amount of water surface area on the Earth is 140 million square miles or 140,000,000 square miles 4.0 x10 -7 = Length of the shortest wavelength of visible light (violet) is meter

ASSESSMENT Write the following in Scientific Notation: ,926,300,00 Convert these back to Standard Form: x x 10 1