1. Significant Figures SPH3U

2. Precision: How well a group of measurements made of the same object, under the same conditions, actually agree with one another. These points are precise with one another but not “accurate”.

3. Accuracy: represents the closeness of a measurement to the true value. Ex: the bulls-eye would be the true value, so these points are accurate.

4. Why Significant Figures? Precision is determined by the instrument we use to take measurements. So, our calculations must be only as precise as the measurements. NOTE : The last digit of any measurement is always a “guess” therefore it is uncertain.

5. Measuring: precision

6. Other instruments…

7. Rounding You will need to round off sig. figs when you multiply, divide, add or subtract. When rounding off to a certain place value, you need to look one place farther. If the next digit is a 5 or higher, you round the digit before it UP. If the next digit is a 4 or lower, you DON”T round up.

8. Using sig figs: The Rules! 1.Digits from 1-9 are always significant. 2.Zeros between two other significant digits are always significant 3.Zeros at the beginning of a number are never significant. 4.Zeros at the end of a number are only significant IF there is a decimal place.

9. Example: Number of sig figs Why? 453kg3 All non-zero digits are always significant. 5057L4 Zeros between 2 sig. dig. are significant. 5.003 Additional zeros to the right of decimal and a sig. dig. are significant. 0.0071 Placeholders are not sig.

10. Problems: Indicate the number of significant figures... 1. 1.235 ______ 2. 2.90______ 3. 0.0987______ 4. 0.450______ 5. 5.00______ 6. 2300______ 7. 230______ 8. 230.0______ 9. 9870345______ 10. 1.00000______

11. 1. 1.235 ___4___ 2. 2.90___3___ 3. 0.0987___3___ 4. 0.450___3___ 5. 5.00___3___ 6. 2300___2___ 7. 230___2___ 8. 230.0___4___ 9. 9870345___7___ 10. 1.00000___6___

12. Round these numbers to 3 significant figures 1)5.8746 = ___________ 2)8008= _____________ 3)24.567= _________ 4)100.04= __________ 5)5634.3999= ____________ 6)1.675 x 10 3 = ____________

13. 1)5.8746 = __5.87_________ 2)8008= ___8010__________ 3)24.567= __24.6_______ 4)100.04= ___100._______ 5)5634.3999= __5630__________ 6)1.675 x 10 3 = ___1.68 x 10 3 _____

14. Multiplying and Dividing RULE: your answer may only show as many significant figures as the multiplied or divided measurement showing the least number of significant digits. Example: 22.37 cm x 3.10 cm = 69.3 (only 3 sig figs allowed)

15. Multiplying and Dividing Practice 1. 42.3 x 2.61______ 2. 32.99 x 0.23______ 3. 46.1 ÷ 1.21______ 4. 23.3 ÷ 4.1______ 5. 0.61 x 42.1______ 6. 47.2 x 0.02______ 7. 47.2 ÷ 0.023______ 8. 100 x 23______ 9. 124 ÷ 0.12______ 10. 120 x 12 ÷ 12.5______

16. 1. 42.3 x 2.61__110.____ 2. 32.99 x 0.23__7.6____ 3. 46.1 ÷ 1.21__38.1____ 4. 23.3 ÷ 4.1__5.7____ 5. 0.61 x 42.1__26____ 6. 47.2 x 0.02__0.9____ 7. 47.2 ÷ 0.023__2100____ 8. 100 x 23__2000____ 9. 124 ÷ 0.12__1000____ 10. 120 x 12 ÷ 12.5__110____

17. Adding and Subtracting: RULE: your answer can only show as many place values as the measurement having the fewest number of decimal places. Example: 3.76 g + 14.83 g + 2.1 g = 20.7 g 3.76 is precise to the hundredths place, 14.83 is precise to the hundredths place, 2.1 is only precise to the tenths place, so we round off the final answer to the tenths place.

18. Adding and Subtracting Practice 1. 2.634 + 0.02______ 2. 2.634 - 0.02______ 3. 230 + 50.0______ 4. 0.034 + 1.00______ 5. 4.56- 0.34______ 6. 3.09- 2.0______ 7. 349 + 34.09______ 8. 234 - 0.98______ 9. 238 + 0.98______ 10. 123.98 + 0.54 - 2.3______

19. 1. 2.634 + 0.02__2.65____ 2. 2.634 - 0.02__2.61____ 3. 230 + 50.0__280____ 4. 0.034 + 1.00__1.03____ 5. 4.56- 0.34__4.22____ 6. 3.09- 2.0__1.1____ 7. 349 + 34.09__383____ 8. 234 - 0.98__233____ 9. 238 + 0.98__239____ 10. 123.98 + 0.54 - 2.3__122.2____

20. Scientific Notation

21. Scientists have developed a shorter method to express very large numbers. Scientific Notation is based on powers of the base number 10.

22. 123,000,000,000 in s.n. is 1.23 x 10 11 The first number 1.23 is called the coefficient. It must be between 1 - 9.99 The second number is called the base. The base number 10 is always written in exponent form. In the number 1.23 x 10 11 the number 11 is referred to as the exponent or power of ten.

23. To write a small number in s.n. ex: 0.00064 First move the decimal after the first real number and drop the zeroes. Ex: 6.4 Next, count the number of places moved from the original decimal spot to the new decimal spot. Ex: 4 Numbers less than 1 will have a negative exponent. Ex: -4 Finally, put it together. Ex: 6.4 x 10 -4

24. Scientific Notation Practice a)0.0826_______________ b)2 630 000_______________ c)945 000_______________ d)1 760 000_______________ e)0.00507_______________ a)1.23 x 10 -4 _______________ b)7.51 x 10 5 _______________ c)3.09 x 10 -3 _______________ d)2.91 x 10 2 _______________ e)9.6 x 10 4 _______________

25. a)0.0826__8.26 x 10-2___ b)2 630 000__2.63 x 106___ c)945 000__9.45 x 105___ d)1 760 000__1.76 x 106___ e)0.00507__5.07 x 10-3___ a)1.23 x 10 -4 __0.000123_____ b)7.51 x 10 5 __751000______ c)3.09 x 10 -3 __0.00309_____ d)2.91 x 10 2 __291_________ e)9.6 x 10 4 __96000_______