1. Scientific Notation Part I 8 th Grade Math By Mr. Laws

2. Goal/Standards 8.EE.4 – 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.

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

4. 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.

5. Power Base of 10 Scientific notation must be written based on the powers of 10. PositiveNegative 10 1 = 1010 -1 = 0.1 10 2 = 10010 -2 = 0.01 10 3 = 1,00010 -3 = 0.001 10 4 = 10,00010 -4 = 0.0001 10 5 = 100,00010 -5 = 0.00001 10 6 = 1,000,00010 -6 = 0.000001 Etc...Etc… Smaller Numbers Larger Numbers

6. What does writing in scientific notation form look like? Base Ten Decimal Number Exponent 1.45 x 10 2

7. Writing from standard form to scientific notation form Number in standard form 1 st Step – look where to place the decimal point. Will it go in the front of the 3 or behind the 2? 2 nd Step – move decimal to the left two places. 382 382. 3.82 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!

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

9. Writing from standard form to scientific notation form Number in standard form Question # 2 – Which way should I move the decimal point, and where do I stop? Answer # 1: It is a small number because the decimal is in the front..000525 Question # 1– Is this a big number or small number? 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 5.25 x 10 -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.

11. Writing from standard form to scientific notation form Practice : Write the following numbers in Scientific notatoin: 1.) 5, 185, 700 2.) 0.0000211 5.1857 x 10 6 2.11 x 10 -5

12. 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 10 5 in standard form: 5.36536000 Move decimal point 5 places to the right, 10 5 = 100,000 5.36 x 10 5 = 536000

13. 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

14. Writing from scientific form to standard form. Practice : Write the following Scientific Notations in standard form: a.) 7.42 x 10 3 = b.) 8.83 x 10 -5 = 7420.0000883

15. Summary 1.What are some important strategies you should remember when writing in scientific notation? 2.What are some important factors to remember when writing from standard for to scientific notation and scientific notation to standard form? 3.Do you have clear understanding on what scientific notation is all about? 4.Are there any more questions you may have about scientific notation