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
1.8x x x x1040

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 by 100)
=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

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
7084
421.00
0.538
5000
5x103
5.0 x103
5000.
5120

16. Copy the examples below and write the number of significant figures
(10)
7084 (4)
(3)
(5)
0.538 (3)
5000 (1)
5x103 (1)
5.0 x103 (2)
(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: g x g=
Ex: g/5.2mL=

18. Addition and Subtraction
Line the numbers up in column form
Ex 1: Ex 2:
Ex 3:

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