1. CHAPTER 3 NOTES Scientific Measurement

2. Measurement Qualitative measurements give results in descriptive, nonnumeric form. (Red balloon, tiny animal) Quantitative measurements give results in a definite form, usually numbers and a unit. (8 cm radius balloon, 6.8 kg animal)

3. Accuracy and Precision Accuracy is how close a single measurement comes to the experimental value (true value). Precision is how close several measurements agree with one another. It is a measure of reproducibility of measurements. Measurements may be precise, yet not be accurate!

4. Accuracy and Precision

5. Scientific Notation A number written as a product of two numbers, a coefficient and a power of ten. 6.3 × 10 -4 4.2 × 10 3 The coefficient must be greater than or equal to 1 and less than 10. 63.0 × 10 -4 should be 6.3 × 10 -3 63.0 × 10 -4 should be 6.3 × 10 -3 0.42 × 10 3 should be 4.2 × 10 2 Multiplication: multiply the coefficients and add the exponents. (3.0 × 10 4 ) × (2.0 × 10 5 ) = 6.0 × 10 9 (3.0 × 10 4 ) × (4.0 × 10 5 ) = 12.0 × 10 9 = 1.2 × 10 10

6. Scientific Notation Division: Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator. (6.0 × 10 4 )÷ (1.0 × 10 5 ) = 6.0 × 10 -1 (3.0 × 10 -3 ) ÷ (4.0 × 10 5 ) = 0.75 × 10 -8 = 7.5 X 10 -9 Addition – make all the exponents the same and add. (5.0 × 10 -1 ) + (5.0 × 10 2 ) + (5.0 × 10 -4 ) 0.50 0.0005 0.50 0.0005 (0.005 × 10 2 ) + (5.0 × 10 2 ) + (0.000005 × 10 2 )= 500.5005

7. Scientific Notation Subtraction – make all the exponents the same and subtract.

8. Significant Figures Significant figures in a measurement include all the digits that are known precisely plus one last digit that is estimated. It is important to consider significance of measurements! Scientists cannot ethically report values that indicate more accuracy than possible. The accuracy of the laboratory measurement devices used determine how accurately those measurements may be reported. Always report measurements one place past the smallest graduation (marked spot).

9. Significant Figures Rules for determining significant figures 1. Every nonzero digit is significant 135 has three significant figures 6.237 has four significant figures 2. Zeros between nonzero digits are significant

10. Significant Figures Zeros appearing in front of nonzero digits are not significant. 0.0024 2 SF 0.00007 1 SF 3. Zeros at the end of a number and to the right of a decimal point are significant 6.980 4 SF

11. Significant Figures Zeros at the end of a number are not significant if they are just place markers.That means no decimal! 100 1 SF 720 2 SF 4. Exact numbers (counts) and defined quantities have infinite significant figures. 

12. Significant Figures in Calculations Answers cannot be more precise than the least precise measurement from which it was calculated. If you are using three measurements in calculations, the value least precisely measured is used to determine how many significant figures can be reported.

13. Addition/Subtraction For addition or subtraction, round the answer to the same number of decimal places as the measurement with the least number of decimal places. 61.2 m + 9.35 m + 8.6 m61.2 9.35 8.6 This result may be79.15 9.35 8.6 This result may be79.15 Reported to 1 decimal place 79.2 m

14. Multiplication/Division For multiplication or division, round the answer to the same number of significant figures as are contained in the measurement with the least number of significant figures. 8.3 m X 2.22 m = 18.426 m 2 This result may be reported to 2 SF because 8.3 contains 2 SF and 2.22 contains 3 SF. 18 m 2

15. SI System Basically, this is the metric system. Know the prefixes Table 3.2, p. 64

16. SI System Length: The basic unit of length in the metric system is the meter Volume: The basic unit of volume is the meter 3 A liter is one cubic decimeter; 1000 mL, 1000 cm 3. A liter is one cubic decimeter; 1000 mL, 1000 cm 3. Mass:The basic unit of mass is the kilogram. We usually use grams in the laboratory Density:Density is mass per unit volume, usually g/mL for liquids; g/cm 3 for solids, and g/L for gases

17. SI System Specific Gravity A comparison of the density of a substance to the density of a reference substance, usually at the same temperature. A comparison of the density of a substance to the density of a reference substance, usually at the same temperature. Water is frequently used as the reference substance Water is frequently used as the reference substance Specific gravity is a unitless value. (g/cm3  g/cm3) Specific gravity is a unitless value. (g/cm3  g/cm3) Specific gravity is commonly used to test antifreeze effectiveness and to check urine for diagnosing diabetes. Specific gravity is commonly used to test antifreeze effectiveness and to check urine for diagnosing diabetes.

18. SI System Temperature Temperature is the degree of hotness or coldness of a substance. Temperature is the degree of hotness or coldness of a substance. The Celsius scale has water’s freezing point at 0° and its boiling point at 100° The Celsius scale has water’s freezing point at 0° and its boiling point at 100° The Kelvin temperature scale has water’s freezing point at 273 and its boiling point at 373 The Kelvin temperature scale has water’s freezing point at 273 and its boiling point at 373 Absolute zero is 0 K Absolute zero is 0 K

19. SI System Error Error is the accepted value minus the experimental value Error is the accepted value minus the experimental value Percent error is the absolute value of the error (accepted – experimental) divided by the accepted times 100. This is the one we use most often. Percent error is the absolute value of the error (accepted – experimental) divided by the accepted times 100. This is the one we use most often. | accepted – experimental |×100 accepted