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.

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

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.

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

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.

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

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.

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.

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

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

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

Scientific Measurement How many significant figures are in each measurement? 123 m 40506 mm 9.8000 x 104 m 22 metersticks 0.070 80 m 98000 m

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.

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

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

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

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. SI Base Units Quantity SI base unit Symbol Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of substance mole mol Luminous intensity candela cd Electric current ampere A

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

Scientific Measurement Small Metric Prefixes Prefix Symbol Factor deci d 0.1 centi c 0.01 milli m 0.001 micro μ 0.000 001 nano n 0.000 000 001 Large Metric Prefixes Prefix Symbol Factor giga G 1 000 000 000 mega M 1 000 000 kilo k 1000 Although, the derived SI unit for volume is m3, we commonly use the liter (L) 1 cm3 = 1 mL

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.

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.

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.

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.

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

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. K = °C + 273 °C = K – 273

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. mass volume Density =

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?

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?

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?