1. CHAPTER 3 SCIENTIFIC MEASUREMENT

2. A measurement is a quantity that has both a number and a unit Quantity represents a size, magnitude, or amount Your height (66 inches), your age (15 years), and your body temperature (37°C)

3. Significant Figures The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated Calculated values must be rounded (estimated last digit)

4. To determine whether a digit in a measured value is significant, you need to apply the following 6 rules: 1.Every nonzero digit in a reported measurement is assumed to be significant 2. Zeros appearing between nonzero digits are significant 3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such place-holding zeros 4. Zeros at the end of a number and to the right of a decimal point are always significant. 5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number 6.There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact. The second situation involves exactly defined quantities such as those found within a system of measurement

5. ATLANTIC vs. PACIFIC RULE (Determining the number of significant figures)

6. Atlantic = decimal point is absent Count the significant figures starting with the first non-zero digit on the right Pacific = decimal point is present Count the significant figures starting with the first non-zero digit on the left

7. Examples: 1.12,300 m 2. 40,506 mm 3. 9.8000 x 10 4 m 4. 0.00220 m 5. 98,000 m

8. PRACTICE TIME! ** Remember** Atlantic...Absent Pacific....Present

9. Rules for Rounding Significant Figures: 1.If the number being examined is less than 5, drop it and all the figures to the right of it. Ex: Round 62.5347 to four significant figures. Answer: 62.53 2. If the number being examined is more than 5, increase the number to be rounded by 1. Ex: Round 3.78721 to three significant figures. Answer: 3.79 3. If the number being examined is 5, round the number so that it will be even Ex: Round 726.835 to five significant figures. Answer: 726.84

10. Addition and Subtraction with Significant Figures The answer should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places Examples: 1. 12.52 meters + 349.0 meters + 8.24 meters = 2. 74.626 meters – 28.34 meters =

11. Round the answer to the same number of significant figures as the measurement with the least number of significant figures Multiplying and Dividing with Significant Figures Examples: 1. 7.55 meters x 0.34 meter = 2. 2.10 meters x 0.70 meter = 3. 2.4526 meters 2 ÷ 8.4 meters = 4. 0.365 meter 2 ÷ 0.0200 meter =

12. Scientific Notation Chemistry requires you to make accurate and often very small or very large measurements Scientific notation makes them more manageable to work with A single gram of hydrogen contains approximately 602,000,000,000,000,000,000,000 hydrogen atoms

13. ✴ In Scientific Notation, a given number is written as the product of two numbers: 1. A coefficient 2. 10 raised to a power (exponent)

14. 1. COEFFICIENT A number greater than or equal to one and less than ten 2. 10 RAISED TO A POWER (exponent) *Positive exponent indicates how many times the coefficient is multiplied by 10 (Number greater than 10) *Negative exponent indicates how many times the coefficient is divided by 10 (Number less than 1)

15. Numbers greater than ten in scientific notation **Exponent is POSITIVE and equals the number of places that the original decimal point has been moved to the left. 6,300,000. = 94,700. = Numbers less than one **Exponent is Negative and equals the number of places the decimal has been moved to the right. 0.000 008 = 0.00736 =

16. PRACTICE.... Write each of these numbers in scientific notation 1. 800,000 = 2. 0.00056 = 3. 9,000,000 = 4. 0.01234 = 5. 9,770,010 =

17. From Scientific to Numerical (Standard) notation The mass of one molecule of water written in scientific notation is 2.99 x 10 –23 g. What is the mass in standard notation? The mass of one molecule of water in standard notation is 0.000 000 000 000 000 000 000 0299 gram PRACTICE: 1.9.8 x 10 4 = 2.9.8 x 10 -4 = 3.1.23 x 10 6 = 4. 7.822 x 10 -5 =

18. Multiplying and Dividing with Scientific Notation When multiplying........ Multiply the coefficients and add the exponents Examples (multiplying): 1. (3 x 10 4 ) x (2 x 10 2 ) = 2. (2.1 x 10 3 ) x (4.0 x 10 –7 ) = 3. (6.2 x 10 4 ) x (2.2 x 10 3 ) =

19. When dividing........ Divide the coefficients and subtract the exponents (numerator - denominator) Examples (dividing): 1. 3.0 x 10 5 6.0 x 10 2 2. 8.0 x 10 -5 2.5 x 10 -4

20. Adding and Subtracting with Scientific Notation If adding or subtracting the exponents must be the same Examples: 1. (5.4 x 10 3 ) + (8.0 x 10 2 ) = 2. (7.1 x 10 –2 ) + (5 x 10 –3 ) = 3. (6.8 x 10 4 ) - (3.2 x 10 6 ) = Move LEFT = ADD exponent Move RIGHT = SUBTRACT exponent

21. Accuracy and Precision Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured Compare to the correct value/measurement Precision is a measure of how close a series of measurements are to one another, irrespective of the actual value Compare the values of two or more repeated measurement Good Accuracy, Good Precision Poor Accuracy, Good Precision Poor Accuracy, Poor Precision

22. DO-NOW Determine what each of these targets show (good/bad accuracy/precision) Perform the following calculations: (2.6 x 10 -5 ) + (8.0 x 10 -2 ) = 1.(2.1 x 10 4 ) x (4.0 x 10 –7 ) =

23. Determining Error Accepted value is the correct value for the measurement based on reliable references Experimental value is the value (you) measured in the lab/experiment The difference between the experimental value and the accepted value is called the ERROR Can be positive or negative Error = Experimental value – Accepted value

24. PERCENT ERROR of a measurement is the absolute value of the error divided by the accepted value, multiplied by 100%. Percent error = Error Accepted value 100% x Example Problem: The boiling point of pure water is measured to be 99.1°C. Calculate the percent error. 1. Determine the experimental and accepted values 2. Calculate the error 3. Calculate the percent error

25. Assume that the correct (accurate) length and width of the index card are 12.70 cm and 7.62 cm respectively. Calculate the percent error for each of your two measurements (refer back to your Do-Now) Review Question:

26. The accepted value of a length measurement is 200 cm, and the experimental value is 198 cm. What is the percent error of this measurement? a. 2% b. −2% c. 1% d. −1% PRACTICE PROBLEM!