Powers of Ten Scale Mr Davis Why do

Powers of Ten / Scale Mr. Davis

Why do we care? n Cannot describe many things in science apart from powers of 10 n Scientific notation useful in Physics, Chemistry, Economics, Programming, Engineering, …

http: //powersof 10. com/film

Scientific Notation By Jenny Erickson

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

Why use scientific notation? n For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. n Numbers expressed in scientific notation can be used in a computation with far greater ease.

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

Which of these are in scientific notation? What are the common equivalents? 1. 0 X 100 10. 2 X 102 0. 1 100 1. 5 x 101

Changing standard form to scientific notation.

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

Continued… n 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 n Given: 289, 800, 000 n Use: 2. 898 (moved 8 places) n Answer: 2. 898 x 108

Example 2 n Given: 0. 000567 n Use: 5. 67 (moved 4 places) n Answer: 5. 67 x 10 -4

Changing scientific notation to standard form.

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

Example 3 n Given: 5. 093 x 106 n Answer: 5, 093, 000 (moved 6 places to the right)

Example 4 n Given: 1. 976 x 10 -4 n Answer: 0. 0001976 (moved 4 places to the left)

How do I convert these to scientific notation? 0. 123456789 1, 000, 000 0. 00000123456789 ( 0. 000 000 123456789)

Multiplying and Dividing

Multiplying in Scientific Notation

Multiplying… n The general format for multiplying is as follows… n (N x 10 x)(M x 10 y) = (N)(M) x 10 x+y n First multiply the N and M numbers together and express an answer. n Secondly multiply the exponential parts together by adding the exponents together. n Finally multiply the two results for the final answer.

Multiplying… n (2. 41 x 104)(3. 09 x 102) Ø 2. 41 x 3. 09 = 7. 45 Ø 4 + 2 = 6 Ø 7. 45 x 106

Dividing in Scientific Notation

Dividing… n The general format for dividing is as follows… n (N x 10 x)/(M x 10 y) = (N/M) x 10 x-y n First divide the N number by the M number and express as an answer. n Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number. n Finally multiply the two results together to get the final answer.

Dividing… § (4. 89 x 107)/(2. 74 x 104) Ø 4. 89 / 2. 74 = 1. 78 Ø 7 – 4 = 3 Ø 1. 78 x 103

Even More Practice n Below is a list of links to games and activities all having to do with scientific notation. – http: //www. aaamath. com/dec 71 idec 2 sci. html – http: //janus. astro. umd. edu/cgibin/astro/scinote. pl – http: //www. sciencejoywagon. com/physicsz one/lesson/00 genral/dectosci. htm

Now take the quiz to test your scientific notation skills! n Click on the link below to take the quiz and then use the answer key for the correct answers. – Quiz – Answers

Quiz Time!!! n Below is a set of links for a quiz on multiplying and dividing numbers in scientific notation, and there is a link to get the answers to the quiz. n Quiz on Multiplying and Dividing n Answers to Quiz