Scientific Measurement

1. Scientific Measurement • A measurement is a quantity that has both a number and a unit • Some numbers encountered in science can be either very large or very small • We use scientific notation to make those numbers easier to work with.

2. Scientific Measurement • In scientific notation, a given number is written as a coefficient and an exponent • The coefficient is a number more than 1, but less than 10 • 6 300 000. • 94 700. • 0.000 008 • 0.00 736

3. Scientific Measurement • In chemistry, the meanings of accuracy and precision are quite different. • Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. • Precision is a measure of how close a series of measurements are to one another, regardless of the actual value.

4. Scientific Measurement • Accuracy = how close you are to the true value • Precision = how consistent are your measurements

5. Scientific Measurement Good Accuracy, Good Precision Poor Accuracy, Good Precision Poor Accuracy, Poor Precision The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

6. Scientific Measurement • Percent error indicates the difference between the accepted and experimental values • Or how accurate a measurement is |Accepted-Experimental| 100 Percent Error = X Accepted Value

7. Scientific Measurement • This estimated number, 22.9°C, has three digits. • The first two digits (2 and 2) are known with certainty, while the rightmost digit (9) has been estimated and involves some uncertainty. • These reported digits all convey useful information, however, and are called significant figures.

8. Scientific Measurement • The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. • There are six rules to determine if a number is significant.

9. Scientific Measurement • Every nonzero digit in a reported measurement is assumed to be significant. 24.7 meters • Zeros appearing between nonzero digits are significant. 7003 meters

10. Scientific Measurement • Leftmost zeros appearing in front of nonzero digits are not significant. 0.0071 meters 0.0901 meters • Zeros at the end of a number and to the right of a decimal point are always significant. 43.00 meters 0.010 meters

11. Scientific Measurement • Zeros at the rightmost end of a measurement without a decimal point are not significant. 7000 meters 27,210 meters To make 7000 meters have four significant figures we must add a decimal point - 7000. meters • There are two situations in which numbers have an unlimited number of significant figures. A number that is counted is exact: 21 students in class Exactly defined quantities: 60 min = 1 hr

12. Scientific Measurement How many significant figures are in each measurement? • 123 m • 40506 mm • 9.8000 x 104 m • 22 metersticks • 0.07080 m • 98000 m

13. Scientific Measurement • In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. • It must be rounded to make it consistent with the measurements from which it was calculated.

14. Scientific Measurement • For an addition or subtraction calculation • The answer should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. a. 12.52 meters + 349.0 meters + 8.24 meters b. 74.626 meters – 28.34 meters

15. Scientific Measurement • For a multiplication and division calculation • The answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures. a. 7.55 meters x 0.34 meter b. 0.365 meter2 ÷ 0.0200 meter

16. Scientific Measurement • The International System of Units (abbreviated SI) is a revised version of the metric system. • The SI units were adopted by international agreement in 1960. • SI units are used for consistency among the scientific community

17. Scientific Measurement • There are seven SI base units. • From these base units, all other SI units of measurement can be derived. • Derived units are used for measurements such as volume, density, and pressure.

18. Scientific Measurement • Each SI unit is based on a measurable standard • They are not arbitrary units • Sometimes it is necessary to modify the base unit using a prefix. • Some prefixes make units larger and others make units smaller

19. Scientific Measurement • Although, the derived SI unit for volume is m3, we commonly use the liter (L) 1 cm3 = 1 mL

20. Scientific Measurement • A conversion factor is a ratio of equivalent measurements. • The measurement in the numerator is equivalent to the measurement in the denominator. • Therefore you actually multiplying by 1 • Conversion factors are useful in solving problems in which a given measurement must be expressed in some other unit of measure.

21. Scientific Measurement • Conversion factors within a system of measurement are defined quantities or exact quantities. • Therefore, they have an unlimited number of significant figures and do not affect the rounding of a calculated answer.

22. Scientific Measurement • Weight and mass are two different measurements • Weight is a force that measures the pull on a given mass by gravity. • Mass is the measure of the amount of matter.

23. Scientific Measurement • Scientists commonly use two equivalent units of temperature, the degree Celsius (˚C) and the kelvin (K). • The Celsius scale sets the freezing point of water at 0°C and the boiling point of water at 100°C. • On the Kelvin scale, the freezing point of water is 273 kelvins (K), and the boiling point is 373 K.

24. Scientific Measurement • The Kelvin scale is based on absolute zero • Absolute zero is the point where particle motion ceases • Absolute zero is 0 Kelvin

25. K = °C + 273 °C = K – 273 Scientific Measurement • Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy. • You simply add or subtract 273, as shown in the following equations.

26. mass Density = volume Scientific Measurement • Density is the ratio of the mass of an object to its volume. • Density is an intensive property • The volume of most substances increases as the temperature increases, while the mass remains the same. • Since density is the ratio of an object’s mass to its volume, the density of a substance generally decreases as its temperature increases. • Water is an important exception.

27. Scientific Measurement Calculating Density A copper penny has a mass of 3.10 g and a volume of 0.35 cm3. What is the density of copper?

28. Scientific Measurement Calculating Density A substance has a density of 9.8 g/ mL. If there is 110 g of that substance, what is it volume?

29. Scientific Measurement Calculating Density A beaker contains 175 mL of a liquid with a density of 0.5 g/mL. What is the liquid’s mass?