Using Scientific Measurements

1. Using Scientific Measurements • The conditions under which a measure-ment is obtained has a tremendous impact on the accuracy of the measurement. • Some balances, rulers, graduated cylinders, and other measuring devices can be moreprecisely readthan others. Pg 29-31 Sec 2-1

2. Which of the measuring devices would provide a more accurate measurement? Why is this one a better device to use for measuring? Pg 44-57 Sec 2-3

3. Using Scientific Measurements • Using a calibrated instrument of measure you can be certain of the accuracy of some of the digits measured. • The last digit of the measurement is however, always questionable • Excluding the last digit would be misleading • With the last digit you have some indication of the value’s likely range • Any measurement reported should consist of the certain digits plus the uncertain digit. • The last digit is uncertain, but it isn’t insignificant… Pg 44-57 Sec 2-3

4. Pg 44-57 Sec 2-3

5. Using Scientific Measurements • Since only the significant digits are reported it is important to be able to determine all the significant digits in a measurement. • There are a set of rules that allow us to determine the significance of any figures in any measurement even if we don’t know the origin of the measurement Pg 44-57 Sec 2-3

6. Measurements: Sig Figs • Nonzero integers always count as significant figures • All other rules apply to zeros… • Zeros appearing between two significant digits are significant (sandwiched zeros) • 40.7 L has three significant figures • 87,009 km has five significant figures • Trailing zeros that are after the decimal are significant zeros • 85.00 g has four significant figures • 9.000 000 000 mm has 10 significant figures • 25.300 sec has five significant figures Pg 44-57 Sec 2-3

7. Measurements: Sig Figs • For this class all other zeros are simply place holders and are significant in their accuracy • You might see some alternative ways to indicate significant digits in a measurement • A dashed line over a zero indicates its significance: • 35OŌ has four significant figures • A decimal after a non-decimal number indicates that all digits are significant: • 35OO. has four significant figures Pg 44-57 Sec 2-3

8. Your Turn… How many significant figures does each of the following measurements have? 2 9.0 km 1 1000 g 3 505 btu 2 0.0024 sec 4 1.040 amps 6 0.000 625 000 kg

9. Measurements: Sig Figs • Just because the calculated answer in your calculator has 8 digits in the answer – doesn’t mean they are all significant • Answers calculated from measurements may not be expressed with more significant digits than any of the original measure- ments • Calculator answers must be rounded to reflect the least accurate measurement Pg 44-57 Sec 2-3

10. Measurements: Sig Figs • There are two scenarios for rounding measurements off depending on if the measurements are multiplied/divided or addition/subtraction. • If the calculation calls for multiplication or division the result must be rounded to contain no more significant figures than are in the measurement with the fewest number of significant figures. • For example: 4 2 (2.4 g/ml)(15.82 ml) 38 g = 37.968 g must be rounded off to 2 sig figs Pg 44-57 Sec 2-3

11. Measurements: Sig Figs • If the calculation calls for addition or subtraction the result must be rounded to have he same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. • For example: 2 4 5.44 m – 2.6103 m = 2.8297 m must be rounded off to 2 decimal places 2.83 m There are also rules for rounding… Pg 44-57 Sec 2-3

12. 400.338 = 400.34 400.333 = 400.33 400.3351 = 400.34 400.3350 = 400.34 400.2250 = 400.22 Pg 44-57 Sec 2-3

13. Measurements: Sig Figs • Only measurements are given significance. • There are some numbers that aren’t considered in terms of significance. • Conversion factors have an infinite number of significant figures (ratios of equal measures, like 1 ft/12 in or 60 sec/1 min) • Exact numbers also have an infinite number of significant figures, like 20 apples or 10 test tubes Pg 44-57 Sec 2-3

14. Your Turn… Carry out each of the mathematical operation. Calculate the area of a crystal surface that measures 1.34 m by 0.7488 m. Calculate how many minutes a project took if the times spent on it each day were 92.5 min, 33.32 min, 25.0 min, 45 min, and 95.33 min. Calculate how many hours the result from #2 would work out to be. 1.00 m, 291 min, 4.85 hrs

15. Measurements: Scientific Notation • In chemistry we will work with very large and very small numbers. 602,200,000,000,000,000,000,000 and 0.000,000,000,000,000,000,000,00165 • Can you imagine using these numbers several times in one set of problems! • Fortunately scientists have come up with a way to get around this problem • Scientific Notation Pg 44-57 Sec 2-3

16. Measurements: Scientific Notation • Any number can be expressed in scientific notation • Any number in scientific notation has two parts to it 6.02 x 1023 Exponent: 10 to the positive integer or negative integer Coefficient: Real number between 1 & 10 but not equal to 10 Pg 44-57 Sec 2-3

17. Scientific Notation: Large Number • For the coefficient half: • To write a number in scientific notation that is greater than 1. • Move the decimal point left until you reach a coefficient greater than 1 but less than 10 and place the decimal point there. • For the exponent half: • Count the number of places the decimal point was moved and the exponent half is 10 raised to that number of places. 5.76506 x 1017 576,506,000,000,000,000 Pg 44-57 Sec 2-3

18. Scientific Notation: Small Number • For the coefficient half: • To write a number in scientific notation that is less than 1. • Move the decimal point right until you reach a coefficient greater than 1 but less than 10 and place the decimal point there. • For the exponent half: • Count the number of places the decimal point was moved and the exponent half is 10 raised to the negative of that number. x 10-16 0.000,000,000,000,000,2697 2.697 Pg 44-57 Sec 2-3

19. Scientific Notation: Small Number • The measurement written in scientific notation is the same number as the original large or small number • The exponent indicates how many times the coefficient would be multiplied or divided by 10 to equal the original measurement • This is the procedure to convert from scientific notation to standard notation 3.14 x 104 is equal to 3.14 x 10 x 10 x 10 x 10 = 31,400 Pg 44-57 Sec 2-3

20. Your Turn… Write the following #’s in sci notation… 3.27 x 104 32,700 1.024 x 106 1,024,000 4.7100 x 10-3 0.004 7100 • Complete the calc. and write the answer in sci notation with the correct # of sig figs… 1.13 x 10-2

21. Scientific Notation 4.587E4/1.2E-3 38225000 On the Calculator █ 2nd function button you push before the EE button Avoid this button like the plague The EE button is 2nd function of the comma button Use this button to enter a negative number Pg 44-57 Sec 2-3

22. Measurements: Percents .71 * 100% 71% = = • In chemistry many of our results will be expressed as a percent. • A piece of a 100 • For instance, the questions answered correctly on a quiz can be written as a percent: 25 correct 35 possible Pg 44-57 Sec 2-3

23. Percents: Percent Error • To determine the accuracy of a measure-ment we calculate the percent error • Percent error: when a measurement is compared to its accepted value |measured-accepted| X 100% accepted Assume in a lab we were expecting to make 5.00g of product; instead we made 4.50g, what is our percent error? Pg 44-57 Sec 2-3

24. Percents: Percent Error |measured-accepted| X 100% % error = accepted Assume in a lab we were expecting to make 5.00g of product; instead we made 4.50g, what is our percent error? |4.50g – 5.00g| X 100% 5.00g 10.0% Pg 44-57 Sec 2-3

25. Your Turn… A block of Zinc metal has the dimensions 5.0 cm X 7.0 cm X 20.0 cm, and its mass is 5.0 kg. What is the density of the Zinc metal in g/mL? Zinc’s density is 7.13 g/cm3, what is the percent error from the lab?