1. WARM UP Algebra 21/22 March 2012 Solving Equations Handout Do FOUR problems, showing all steps. Show your CHECK by substituting back into the original. - get a calculator - put your text and binder on your desk

2. objectives Students will be able to write large numbers in scientific notation and in standard form. Students will take notes, participate in class discussion and use think-pair-share. Homework due Friday pg. 357: 1- 4, 11, 15

3. Review exponents 5x 5 = 5 1 ∙x 2 = 5∙x∙x∙x∙x∙x (5x) 5 = (5x)(5x)(5x)(5x)(5x) How are they different? PRACTICE- expand: 1)7x 4 2)10x 4 3)4x 7

4. Working with BIG numbers Meredith is doing a report on stars and wants to estimate the total number of stars in the universe. She reads that astronomers estimate there are at least 125 billion galaxies in the universe. An encyclopedia says that the Milky Way, Earth’s galaxy, is estimated to contain more than 100 billion stars. Estimate the total number of stars in the universe.

5. Things to Remember From zero to the right the numbers get BIGGER. From zero to the left the numbers get SMALLER.

6. Numbers On a Number Line

7. 1) 2) Place the following numbers on the number line. a)0.9 b) 2.7 c) 5.56 d) 9.9 e) 7.7

8. 3) Write down two very, very large numbers. 4) Write down 2 very, very small positive (+) numbers. 5) List (write down) 15 numbers between 1 and 10.

9. Scientific Notation

10. In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg Scientific Notation

11. Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 x 602000000000000000000000 ??????????????????????????????????

12. Scientific Notation: A way of representing very large or very small numbers in the form: a x 10 n INTEGER  a is a number between 1 and 10 (Yes decimal numbers such as 0.7 or 2.5 or 7.7).  n is an integer ( whole numbers like – 2 or 11 but decimal). TIMES

13. In other words: Scientific notation expresses a number in the form: a x 10 n 1  a  10 n is an integer

14. CLASSWORK Do Now Identify “a” and “n” from each expressions. 1) 2) 3) a= _______ a= _______ a=_________ n = ______ n=________ n=_________

15. CLASSWORK Do Now: Investigation: A Scientific Quandary Page 355 Steps 1 and 2 BE READY TO SHARE

16. . 2 500 000 000 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point 1 2 3 45 6 7 8 9 Step #4: Re-write in the form M x 10 n SCIENTIFIC NOTATION FOR LARGE NUMBERS

17. 2.5 x 10 9 The exponent is the number of places we moved the decimal.

18. LET DO ONE TOGETHER Write the following number in scientific notation. Two-hundred-and eighty million 280, 000, 000 answer: 2.8 x 10 8

19. 0.0000579 Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n 1 23 4 5 SCIENTIFIC NOTATION FOR SMALL NUMBER

20. 5.79 x 10 -5 The exponent is negative because the number we started with was less than 1.

21. VIDEO http://www.youtube.com/watch?v=H578qUeo BC0

22. Example: Large numbers Given: 289,800,000 Use: 2.898 -- between 1 and 10 (moved 8 places) Answer: 2.898 x 10 8

23. Example 2 Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10 -4 Use: 5.67 - a number between 1 and 10 (moved 4 places) Answer: 5.67 x 10 -4 Negative because it is a small number

24. Example 3 Given: 5.093 x 10 6 HOW? ADD 6 decimal places to 5.093 Answer: 5,093,000 (moved 6 places to the right) positive exponent means BIGGER NUMBER

25. Example 4 Write in scientific notation 800,000 x 10 4 Rewrite 800,000 as 8.0 x 10 5 800,000 x 10 4 = 8.0 x 10 5 x 10 4 = 8.0 x 10 5+4 = 8.0 x 10 9

26. LET’S DO ONE TOGETHER Given: 0.000567 Answer: 5.67 x 10 -4 Use: 5.67 (moved 4 places) Answer: 5.67 x 10 -4

27. Let’s do one together. Do Handout 6.4 Do your work on a separate paper if you need more room. Be ready to show your work to the class.

28. CLASSWORK paper- debrief SUMMARY: 1)Write five things you learned or relearned today. 2) Make up a question someone might ask about exponents.

29. Glencoe practice http://www.glencoe.com/sec/math/algebra/al gebra1/algebra1_01/pdf/0903.pdf http://www.youtube.com/watch?v=H578qUeo BC0