BY: C L A U D I A H Y S A & D O U G S T R I C K L E

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 109 = 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:–0.00036 = –3.6 × 10–4 0.00036 = 3.6 × 10–4

36,000 = 3.6 × 104 –36,000 = –3.6 × 104

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 = 1.2x109

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 10-7 = 0.00000065

REAL WORLD EXAMPLES

• 7 x109= Population of the world is around 7 billion written out as 7,000,000,000

• 1.0 x1014= Approximate number of cells in the human body is 100 trillion or 100,000,000,000,000

• 9.3 x107= Distance from the Earth to the sun is 93 million miles or 93,000,000 miles

• 1.4 x108= 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 0.0000004 meter

ASSESSMENT

Write the following in Scientific Notation:1. 10012. 533. 6,926,300,00

Convert these back to Standard Form:4. 1.92 x 103

5. 3.051 x 101