Scientific Notation

1. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

2. The Distance From the Sun to the Earth 93,000,000 miles

3. Step 1 • Move decimal left • Leave only one significant number in front of the decimal 93,000,000 = 9.3000000

4. Step 2 • Write number without zeros 93,000,000 = 9.3

5. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten • The power of ten is the letter “E” (exponential) for your calculators.

6. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

7. 93,000,000 - Standard Form 9.3 x 107 - Scientific Notation 4567 x 10-5 - Scientific Notation .04567 - Standard Form

8. What if it has a decimal? Move the decimal to the right after the first significant (not a zero) number. • .000,000,043 --- Standard Form • 4.3 x 10-8 - Scientific Notation

9. 1.) 9.85 x 10-4? = 2.) 64,100,000,000 = 3.) 2.79 x 10-6 = 4.) 431,200,000 = 5.) .000,0496= .000,985 6.41 x1010 .000,00279 4.31 x 108 4.96 x 10-5 Practice Problems Write in scientific notation or standard form.

10. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • .000,000,000,870 = ______x 10-10 • 90,000,000,000 = _____ x 1010 Answers 3) 9.0 x 1010 2)8.70 x 10-10 • 7.34 x 108

11. Complete Practice Problems Write in scientific notation . • 50,000 • 7,200,000 • .000,000,802 Answers 1) 5.0 x 104 2) 7.2 x 106 3) 8.02 x 10-7

12. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

13. 6.27 x 106 9.01 x 104 4.603 x 108 9.94 x 102 6,270,000 90,100 460,300,000 994 Write in Standard Form Move the decimal to the right.

14. 3.89 x 10-7 3.872 x 10-6 8.940 x 10-3 4.931 x 10-3 23.8761 x 10-4 .000,000,389 .000,003,872 .00894 .004931 .00238761 Write in Scientific Notation Move the decimal to the left.

15. 0.07882 = 0.000,00272338 = 118000 = 87200 = 0.000,02786 = 0.000,000664 = 450 = 74171.7 = 770 = 0.000,0085 = 7.882 × 10-2 2.72338 × 10-6 1.18 × 105 8.72 × 104 2.786 × 10-5 6.64 × 10-7 4.5 × 102 7.41717 × 104 7.7 × 102 8.5 × 10-6 Write in Scientific Notation

16. 1. What is this number in standard form? 6.73 x 10-6 • 6,730,000 • 0.00000673 • 0.0000673 • 673,000

17. 2. When the exponent is positive you move the decimal to the: • Left • Right • Top • bottom

18. 3. What does your calculator use to designate as a power of ten for scientific notation • 10 • P • G • E

19. 4. Why is scientific notation important when dealing with astronomy? • They want to • They are really big numbers and they are lazy • Planets and stars are really far away so using scientific notation makes it easier to record the numbers • It helps with Inverse Square Law

20. 5. Which of these numbers shows 1 million in scientific notation? • 1 x 103 • 1 x 104 • 1 x 107 • 1 x 106

21. 6. Changer 1204.6 in scientific notation? • 1.2 x 103 • 120 x 10-2 • 12 x 102 • 1204 x 100

22. 7. Change 17.8 in scientific notation? • 1.78 x 102 • 1.78 x 101 • 1.78 x 10-1 • 1.78 x 10-2

23. 8. Change 567,310 in scientific notation? • 567 x 103 • 56.7 x 105 • 5.67310 x 105 • 5 x 106

24. 9. Convert 8.36 x 102 in scientific notation? • 83600 • 8360 • 836 • 836000

25. 10. Convert 9.16 x 106 in scientific notation? • 0.000000916 • 0.000916 • 9,160 • 9,160,000