1. 1 1-6 Working with Numbers

2. 2 Significant Digits (sig fig's) - certain digits and the estimated digit of a measurement. Significant Digits (sig fig's) - certain digits and the estimated digit of a measurement. Rules of Sig Fig's (Atlantic-Pacific Rule) Rules of Sig Fig's (Atlantic-Pacific Rule)

3. 3 P of pacific stands for decimal point present If a decimal point is present you start on the left side of the number, like the pacific ocean is on the left side of America. Read through the number until you hit a non zero number. This begins the significant numbers. If a decimal point is present you start on the left side of the number, like the pacific ocean is on the left side of America. Read through the number until you hit a non zero number. This begins the significant numbers.

4. 4 A of Atlantic stands for decimal point absent If the decimal point is absent you begin counting all non-zero digits from the right or Atlantic side of the number. If the decimal point is absent you begin counting all non-zero digits from the right or Atlantic side of the number.

5. 5 Significant Figures Rules Table p. 47

6. 6 Rules for Significant Zeros Animation

7. 7 Examples 34.067g 34.067g  5 sig figs 0.0007458ml 0.0007458ml  4 sig figs  4 sig figs 0.009070g 0.009070g  4 sig figs  4 sig figs

8. 8 Examples 2030cm 2030cm  3 sig figs 2007dm 2007dm  4 sig figs 19,000,000,000g 19,000,000,000g  2 sig figs

9. 9 Practice Problems 0.0026701m 0.0026701m  5 sig figs 19.0550kg 19.0550kg  6 sig figs 3500V 3500V  2 sig figs 1,809,000L 1,809,000L  4 sig figs

10. 10 Sig Fig's in Calculations Exact numbers or conversions do not count as sig figs Exact numbers or conversions do not count as sig figs In multiplication or division the answer can only have as many sig figs as the number with the least amount of sig figs. In multiplication or division the answer can only have as many sig figs as the number with the least amount of sig figs.

11. 11 Example: Volume = length x width x height Find the volume an object 10.876m x 1.34m x 13.22m Find the volume an object 10.876m x 1.34m x 13.22m on your calculator you will get a number like 192.6661648 on your calculator you will get a number like 192.6661648 The correct answer would be 193m 3 The correct answer would be 193m 3  1.34m only has 3 sig figs

12. 12 In addition or subtraction the largest uncertainty determines the number of sig figs In addition or subtraction the largest uncertainty determines the number of sig figs

13. 13 Example Add 34.50g + 3.2345g + 671.1g + 25.345g = 734.7745g Add 34.50g + 3.2345g + 671.1g + 25.345g = 734.7745g The largest uncertainty is 0.1 therefore the answer could have one digit after the decimal. The correct answer would be 734.8g after rounding up The largest uncertainty is 0.1 therefore the answer could have one digit after the decimal. The correct answer would be 734.8g after rounding up

14. 14 Practice Problems 6.15m x 4.026m = 6.15m x 4.026m = 12.7km / 3.0 = 12.7km / 3.0 = 150ml + 76.9ml + 209ml + 0.036ml = 150ml + 76.9ml + 209ml + 0.036ml = (35.6L + 2.4L) / 4.803 = (35.6L + 2.4L) / 4.803 = 2.542m x (16.408m - 3.88m) = 2.542m x (16.408m - 3.88m) =

15. 15 Scientific Notation M x 10 n Greater than or equal to 1 but less than 10 A whole number A negative exponent means the number is small A positive exponent means the number is large

16. 16 Scientific Notation Example 19,000,000ml Example 19,000,000ml  You can only have two sig fig's  1.9 x 10 7 Example 0.0004569g Example 0.0004569g  3 sig figs  4.57 x 10 -4 g  4.57 x 10 -4 g

17. 17 Sample Problems 32,700 32,700  3.27 x 10 4  3.27 x 10 4 1,024,000 1,024,000  1.024 x 10 6 0.0047100 0.0047100  4.7100 x 10 -3 0.000000003901 0.000000003901  3.901 x 10 -9

18. 18 Percent Error % Error = measured – accepted x 100 % Error = measured – accepted x 100 accepted accepted

19. 19 Sample Problem In class Friday we calculated the density of water. Many students reported values other than the accepted value of 1g/ml or 1g/cm 3 In class Friday we calculated the density of water. Many students reported values other than the accepted value of 1g/ml or 1g/cm 3 Lets say you calculated the density of water to be.9g/ml Lets say you calculated the density of water to be.9g/ml % Error = 0.9 - 1 x 100 = 10% error % Error = 0.9 - 1 x 100 = 10% error 1 1

20. Chapter 2 Section 2 Units of Measurements pages 33-43 20 Density The ratio of mass to volume The ratio of mass to volume D = M / V D = M / V Unit = kg/m 3 or g/cm 3 = g/mL Unit = kg/m 3 or g/cm 3 = g/mL A characteristic physical property A characteristic physical property Can be used to identify a substance Can be used to identify a substance Varies with temperature Varies with temperature

21. Chapter 2 Section 2 Units of Measurements pages 33-43 21 Density Table p. 38

22. 22 Density Formula Animation

23. Chapter 2 Section 2 Units of Measurements pages 33-43 23 Density 1. What is the density of a block of marble that occupies 310 cm 3 and has a mass of 853 g? 2. Diamond has a density of 3.26g/cm 3. What is the mass of a diamond that has a volume of 0.351 cm 3 ? 3. What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given the density of mercury is 13.6 g/mL? p. 40 1. 2.75 g/cm 3 2. 1.14 g 3. 5.60 mL