Scientific Notation

1. Scientific Notation

2. Practice Quiz Put the following in order from smallest to largest. • 1.8x10-5 • 8.7x1024 • 0.7x10-3 • 1.4x1040

3. Answers Smallest Largest 1.8x10-5 0.7x10-3 8.7x1024 1.4x1040

4. Scientists (and those studying science) frequently must deal with numbers that are very large or very small.

5. Instead of wasting time by writing many zeros before and after numbers, a method of writing very large and very small numbers was invented. It is called scientific notation.

6. Rules • The first figure is a number from 1 to 9. • The first figure is followed by a decimal point and then the rest of the figures. • Then multiply by the appropriate power of 10.

7. Are these numbers written in scientific notation? • 60.5x105 • 6.05x106 • 0.65x10-2 • 4.252

8. Examples • 425=4.25x102 (102 is the same as 100, so you are really multiplying 4.25 by 100) • 0.00098=9.8x10-4 (10-4 is the same as 1/1000, so you are really multiplying 9.8 by 1/1000)

9. Practice Write the following in scientific notation: • 36000 • 0.0135 • 3951 • 0.632 • 0.00000090

10. Answers • 3.6x104 • 1.35x10-2 • 3.951x103 • 6.32x10-1 • 9.0x10-7

11. Math is easy-use your calculator!!! • 4.2x104kg + 7.9x103kg= • 5.23x106mm x 7.1x10-2mm= • 5.44x107g/8.1x104mol=

12. Answers • 4.99x104 kg • 3.71x105mm2 • 6.72x102 g/mol

13. Significant Figures

14. Rules • All non zero digits are significant Ex: 127 • Zeros between significant digits are always significant (sandwich zeros) Ex: 106 • Leading zeros are never significant (placeholder zeros) Ex: 0.005 • Trailing zeros are significant only if there is a decimal in the number Ex: 25.30

15. Copy the examples below and write the number of significant figures • 7623142516 • 7084 • 0.00761 • 421.00 • 0.538 • 5000 • 5x103 • 5.0 x103 • 5000. • 5120

16. Copy the examples below and write the number of significant figures • 7623142516 (10) • 7084 (4) • 0.00761 (3) • 421.00 (5) • 0.538 (3) • 5000 (1) • 5x103 (1) • 5.0 x103 (2) • 5000. (4) • 5120 (3)

17. Multiplication and Division • The final answer should have the same number of sig figs as the measurement having the smallest number of sig figs Ex: 10.305g x 0.00320g= Ex: 3.64928g/5.2mL=

18. Addition and Subtraction • Line the numbers up in column form Ex 1: 3.461728 Ex 2: 467.384 14.91 -2.384 0.98001 + 5.2631 Ex 3: 564321 - 264321

19. Significant Figures Song To the tune of Three Blind Mice

20. Verse 1 • Addition and Subtraction line numbers up in columns (Repeat) • Make sure the decimals are aligned right, Take off the numbers that are on the right • To get the sig figs (Repeat)

21. Verse 2 • Multiplication and division count the numbers (Repeat) • Find the one that is the least That’s the number, the rest will cease • To get the sig figs (Repeat)

22. Complex Conversions

23. #1 A heater gives off heat at a rate of 330kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal=4.184J)

24. #1 Answer 4.7x103 kcal/h

25. #2 A water tank leaks water at the rate of 3.9mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year?

26. #2 Answer 34L/yr

27. #3 At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?

28. #3 Answer 1670km/hr 4.02x104 km/d

29. Density

30. Formula • Density=Mass/Volume • D=m/V • If you know the density triangle, you can get the formulas for m and V. • The units of density are always going to have a division sign in them. Ex: g/mL

31. Question 1 A block has a volume of 25.3cm3. Its mass is 21.7g. Calculate the density of the block.

32. Answer 0.858g/cm3

33. Question 2 Isopropyl alcohol has a density of 0.785g/mL. What volume should be measured to obtain 20.0g of the liquid?

34. Answer 25.5mL

35. Question 3 Ethanol has a density of 0.785g/mL. If you have 105mL, how much mass will it have?

36. Answer 82.4g