Writing in Scientific Notation 8th Grade Math By Mr. Laws

Goal/Standards 8.EE.3 – Use numbers expressed in the form of a single a single digit times in integer power of 10 to estimated very large or very small quantities, and to express how many times as much one is that the other.

Essential Question: Using Math Principle, explain how I can use scientific notation to represent very large or very small numbers?

What is scientific notation? Scientific notation is a method used in math or science to write out very large or very small quantities. Scientific notation can be written in standard form, which are numbers or scientific notation form.

Power Base of 10 Positive Negative 101 = 10 10-1 = 0.1 102 = 100 Scientific notation must be written based on the powers of 10. Positive Negative 101 = 10 10-1 = 0.1 102 = 100 10-2 = 0.01 103 = 1,000 10-3 = 0.001 104 = 10,000 10 -4 = 0.0001 105 = 100,000 10-5 = 0.00001 106 = 1,000,000 10-6 = 0.000001 Etc... Etc… Larger Numbers Smaller Numbers

What does writing in scientific notation form look like? 1.45 x 102 Exponent Decimal Number Base Ten

Writing from standard form to scientific notation form Number in standard form 382 382. 3.82 1st Step – look where to place the decimal point. Will it go in the front of the 3 or behind the 2? 2nd Step – move decimal to the left two places. S.N. Rule # 1 – when moving decimals the first number in the decimal must either equal to 1, or be more than 1 but less than 10!

3.82 10 Writing from standard form to scientific notation form x 2 3rd step - multiply 3.82 by base of 10. 4th step - since you move the decimal point two places to the left, the base of 10 has a power of 2.

Writing from standard form to scientific notation form Number in standard form .000525 5.25 Question # 1– Is this a big number or small number? Answer # 1: It is a small number because the decimal is in the front. Question # 2 – Which way should I move the decimal point, and where do I stop? Answer # 2: You have to move the decimal to the right and stop after 5.

5.25 10 Writing from standard form to scientific notation form x -4 Same steps – multiply 5.25 by the base of 10; however since you move the decimal point four places to the right and the number is below 1, the base of 10 has a negative power of 4.

Writing from standard form to scientific notation form Practice : Write the following numbers in Scientific notatoin: 1.) 5, 185, 700 5.1857 x 106 2.11 x 10-5 2.) 0.0000211

Writing from scientific form to standard form. Rule# 2 – When multiplying by a positive base power of 10, the decimal point moves to the right. Write 5.36 x 105 in standard form: Move decimal point 5 places to the right, 105 = 100,000 5.36 536000 5.36 x 105 = 536000

Writing from scientific form to standard form. Rule# 3 – When multiplying by a negative base power of 10, the decimal point moves to the left. Write 3.24 x 10-7 in standard form: 3.24 .000000324 Move decimal point 7 places to the left, 10-7 = .0000001 3.24 x 10-7 = .000000324

Writing from scientific form to standard form. Practice : Write the following Scientific Notations in standard form: a.) 7.42 x 103 = 7420 b.) 8.83 x 10-5 = .0000883

Summary What are some important strategies you should remember when writing in scientific notation? What are some important factors to remember when writing from standard for to scientific notation and scientific notation to standard form? Do you have clear understanding on what scientific notation is all about? Are there any more questions you may have about scientific notation