2. Significant Figures Integrated Science Dr. May

3. Significant Figures Numbers obtained from measurements are never exact values Numbers obtained from measurements are never exact values Maximum precision includes all digits that are known plus one estimated Maximum precision includes all digits that are known plus one estimated The digits used to express a measured quantity are known as significant figures The digits used to express a measured quantity are known as significant figures

4. Evaluating Zero In any measurement all nonzero numbers are significant In any measurement all nonzero numbers are significant 65.6291 grams has six significant figures 65.6291 grams has six significant figures Zeros may or may not be significant depending on their position in the number Zeros may or may not be significant depending on their position in the number

5. Zero is Significant When It is between nonzero digits It is between nonzero digits 2.05 has three significant figures 2.05 has three significant figures 61.009 has five significant figures 61.009 has five significant figures

6. Zero is Significant When It is at the end of a number that includes a decimal point It is at the end of a number that includes a decimal point 0.500 has three significant figures 0.500 has three significant figures 25.160 has five significant figures 25.160 has five significant figures 200. has three significant figures 200. has three significant figures

7. Zero is Not Significant When It comes before the first nonzero digit (These zeros are used to place the decimal) It comes before the first nonzero digit (These zeros are used to place the decimal) 0.0025 has two significant figures 0.0025 has two significant figures 0.00708 has three significant figures 0.00708 has three significant figures

8. Zero Is Not Significant When It comes at the end of a number that contains no decimal point It comes at the end of a number that contains no decimal point 1000 has one significant figure 1000 has one significant figure 590 has two significant figures 590 has two significant figures

9. Determine Significant Figures 4.5 inches= 4.5 inches= 3.025 feet= 3.025 feet= 125.0 meters= 125.0 meters= 0.001 miles= 0.001 miles= 25.0 grams= 25.0 grams= 100,000 people= 100,000 people= 205 birds= 205 birds= 2 4 4 1 3 1 3

10. Rounding Off Numbers Integrated Science Dr. May

11. Rounding Off Numbers When we do calculations we often obtain answers with more digits than are justified When we do calculations we often obtain answers with more digits than are justified We need to drop the excess digits to express the answer in the proper number of significant figures We need to drop the excess digits to express the answer in the proper number of significant figures This is called rounding off numbers This is called rounding off numbers

12. Rounding Off Numbers - Rule 1 When the first digit after those you want to retain is 4 or less, that digit and all others to the right are dropped. When the first digit after those you want to retain is 4 or less, that digit and all others to the right are dropped. The last digit retained is not changed The last digit retained is not changed Round 1.00629 to 4 significant figures Round 1.00629 to 4 significant figures 1.00629 = 1.006 1.00629 = 1.006

13. Rounding Off Numbers - Rule 2 When the first digit after those you want to retain is 5 or greater, that digit and all others to the right are dropped. When the first digit after those you want to retain is 5 or greater, that digit and all others to the right are dropped. The last digit retained is increased by 1 The last digit retained is increased by 1 Round 18.02500 to four significant figures Round 18.02500 to four significant figures 18.02500 = 18.03 18.02500 = 18.03

14. Round Off As Indicated 42.246 (four)= 42.246 (four)= 88.015 (four)= 88.015 (four)= 0.08965 (three)= 0.08965 (three)= 0.08965 (two)= 0.08965 (two)= 225.3 (three)= 225.3 (three)= 14.150 (three)= 14.150 (three)= 42.25 88.02 0.0897 0.090 225 14.2

15. Scientific Notation Integrated Science Dr. May

16. Very large and very small numbers can be simplified and conveniently written using a power of 10 Very large and very small numbers can be simplified and conveniently written using a power of 10 4,500,000,000 (4.5 billion) can be written 4,500,000,000 (4.5 billion) can be written 4.5 x 10 9 Writing a number as a power of 10 is called scientific notation Writing a number as a power of 10 is called scientific notation

17. Powers of Ten 10 0= 10 0= 10 1= 10 1= 10 2= 10 2= 10 3= 10 3= 10 4= 10 4= 10 5= 10 5= 10 6= 10 6= 1 10 100 1,000 10,000 100,000 1,000,000

18. Negative Powers of Ten 10  0= 10  0= 10  1= 10  1= 10  2= 10  2= 10  3= 10  3= 10  4= 10  4= 10  5= 10  5= 10  6= 10  6= 1 0.1 0.01 0.001 0.0001 0.00001 0.000001

19. Number to Scientific Notation Convert 0.000056 to 5.6 x 10  5 Convert 0.000056 to 5.6 x 10  5 Choose the number between 1 and 10 = 5.6 Choose the number between 1 and 10 = 5.6 Multiply by 10: 5.6 x 10 Multiply by 10: 5.6 x 10 If the number is < 1 use a negative exponent If the number is < 1 use a negative exponent 5.6 x 10  Count the spaces the decimal was moved Count the spaces the decimal was moved 5.6 x 10  5

20. Number to Scientific Notation Convert 560,000 to 5.6 x 10 5 Convert 560,000 to 5.6 x 10 5 Choose the number between 1 and 10 = 5.6 Choose the number between 1 and 10 = 5.6 Multiply by 10: 5.6 x 10 Multiply by 10: 5.6 x 10 If the number is > 1 use a positive exponent If the number is > 1 use a positive exponent 5.6 x 10 Count the spaces the decimal was moved Count the spaces the decimal was moved 5.6 x 10 5

21. Scientific Notation to Number Convert 5.6 x 10 5 to 560,000 Convert 5.6 x 10 5 to 560,000 Write the significant figures = 56 Write the significant figures = 56 The exponent is positive, the number is > 1 The exponent is positive, the number is > 1 Add zeros to place the decimal 5 spaces Add zeros to place the decimal 5 spaces to the right 560,000. 560,000.  5    5  

22. Scientific Notation to Number Convert 5.6 x 10  5 to 0.000056 Convert 5.6 x 10  5 to 0.000056 Write the significant figures = 56 Write the significant figures = 56 The exponent is negative, the number is < 1 The exponent is negative, the number is < 1 Add zeros to place the decimal 5 spaces Add zeros to place the decimal 5 spaces to the left 0.000056 0.000056   5    5 

23. Convert To Scientific Notation 0.00034= 0.00034= 0.00145= 0.00145= 0.0000985= 0.0000985= 0.016856= 0.016856= 0.0003967= 0.0003967= 0.0000002= 0.0000002= 0.00040= 0.00040= 0.00600= 0.00600= 3.4 x 10  4 1.45 x 10  3 9.85 x 10  5 1.6856 x 10  2 3.967 x 10  4 2 x 10  7 4.0 x 10  4 6.00 x 10  3

24. Convert To Scientific Notation 3400 = 3400 = 36,000,000 = 36,000,000 = 367,800,000,000 = 367,800,000,000 = 58 = 58 = 65789 = 65789 = 1,000,000,000 = 1,000,000,000 = 2,000 = 2,000 = 3.4 x 10 3 3.6 x 10 7 3.678 x 10 11 5.8 x 10 1 6.5789 x 10 4 1 x 10 9 2 x 10 3

25. Convert to Numerical Values 7.4 x 10 3 = 7.4 x 10 3 = 5.6 x 10 5 = 5.6 x 10 5 = 6.674 x 10 10 = 6.674 x 10 10 = 5.1 x 10 4 = 5.1 x 10 4 = 6.5559 x 10 1 = 6.5559 x 10 1 = 3.64186 x 10 4 = 3.64186 x 10 4 = 1 x 10 3 = 1 x 10 3 = 7,400 560,000 66,740,000,000 51,000 65.559 36,418.6 1,000

26. Convert to Numerical Values 7.4 x 10  3 = 7.4 x 10  3 = 5.6 x 10  5 = 5.6 x 10  5 = 6.674 x 10  8 = 6.674 x 10  8 = 5.1 x 10  4 = 5.1 x 10  4 = 6.5559 x 10  1 = 6.5559 x 10  1 = 3.641 x 10  4 = 3.641 x 10  4 = 1 x 10  3 = 1 x 10  3 = 0.0074 0.000056 0.00000006674 0.00051 0.65559 0.0003641 0.001

27. The End This presentation was created for the benefit of our students by the Science Department at Howard High School of Technology This presentation was created for the benefit of our students by the Science Department at Howard High School of Technology Please send suggestions and comments to rmay@nccvt.k12.de.us Please send suggestions and comments to rmay@nccvt.k12.de.us