Scientific Notation

What is scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise.

Scientific notation consists of two parts: A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer

Are these numbers in scientific notation? x x 10 4/ x x Yes No Yes No

Powers of Ten When multiplying or dividing by powers of ten, we can use a shortcut to solve. Multiplying: 1. count the number of zeros 2. move decimal point that number of places to the right Dividing: 1. count the number of zeros 2. move decimal point that number of places to the left

Exponents of Ten When powers of ten are expressed as exponents, the exponent represents the number of zeros. Ex = 100,000 Ex = 1,000,000,000,000

Examples 38 x 10 2 = 2.43 x 10 7 = x 1,000 = 12 ÷ 10,000= 93.6 ÷ 10 2 = 3,800 24,300, ,200,000 9,360

Changing standard form to scientific notation.

To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Example 1 Given: 289,800, Decimal point moved 8 places Original number is greater than 1 Answer: x 10 8

Example 2 Given: Decimal point moved 4 places Original number is less than 1 Answer: 5.67 x 10 -4

Convert to Scientific Notation ,298, x x x x 10 2

Changing scientific notation to standard form.

To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent of 10. Move the decimal point to the left for negative exponent of10. (Use zeros to fill in places.)

Example 3 Given: x 10 6 moved 6 places to the right Fill in extra places with zeros Answer: 5,093,000

Example 4 Given: x moved 4 places to the left Fill in extra places with zeros Answer:

Convert to standard form x x x , ,000,000

Using the Calculator In order to enter a number in scientific notation into the calculator, we use the EE button Ex x 10 4 enter the number : 3.26 click the 2 nd key click the EE (above the x -1 ) enter the exponent : 4 click equals

Using the Calculator When a calculation yields a very large or very small number, some calculators will give the answer in scientific notation. If the calculator says a EE b –The a is the number –The b is the exponent of ten Ex. 4.3 EE -7 = 4.3 x 10 -7