The number of stars in a galaxy is an example of an estimate that should be expressed in scientific notation.

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1 3.1 Using and Expressing Measurements A measurement is a quantity that has both a number and a unit. Using and Expressing Measurements In scientific notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power. The number of stars in a galaxy is an example of an estimate that should be expressed in scientific notation. Accuracy, Precision, and Error Accuracy and Precision 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. Accuracy, Precision, and Error Determining Error The accepted value is the correct value based on reliable references. The experimental value is the value measured in the lab. The difference between the experimental value and the accepted value is called the error. Accuracy, Precision, and Error The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%. Significant Figures in Measurements Why must measurements be reported to the correct number of significant figures? Significant Figures in Measurements The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. (use rules from your green sheet)

2 Significant Figures in Measurements Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation. Significant Figures in Measurements ""#$%&"'#()#*+"")#,-+.#/(01#2-).(%/# Significant Figures in Calculations How does the precision of a calculated answer compare to the precision of the measurements used to obtain it? Significant Figures in Calculations In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. The calculated value must be rounded to make it consistent with the measurements from which it was calculated. Significant Figures in Calculations Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. 3.2 Significant Figures in Calculations Multiplication and Division In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements Measuring with SI Units All measurements depend on units that serve as reference standards. The standards of measurement used in science are those of the metric system. The International System of Units (abbreviated SI, after the French name, Le Système International d Unités) is a revised version of the metric system. Measuring with SI Units The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole. Units of Length In SI, the basic unit of length, or linear measure, is the meter (m). For very large or and very small lengths, it may be more convenient to use a unit of length that has a prefix.

3 Common metric units of length include the centimeter, meter, and kilometer. Units of Volume The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge. This volume is the cubic meter (m) 3. A more convenient unit of volume for everyday use is the liter, a non-si unit. Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter. The volume of 20 drops of liquid from a medicine dropper is approximately 1 ml. A sugar cube has a volume of 1 cm 3. 1 ml is the same as 1 cm 3. Units of Mass

4 The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass. A gram (g) is 1/1000 of a kilogram; the mass of 1 cm 3 of water at 4 C is 1 g. Common metric units of mass include kilogram, gram, milligram, and microgram. Weight is a force that measures the pull on a given mass by gravity. The astronaut shown on the surface of the moon weighs one sixth of what he weighs on Earth. Units of Temperature Temperature is a measure of how hot or cold an object is. Thermometers are used to measure temperature. Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. On the Celsius scale, the freezing point of water is 0 C and the boiling point is 100 C. On the Kelvin scale, the freezing point of water is kelvins (K), and the boiling point is K. The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to C. Because one degree on the Celsius scale is to one kelvin on the Kelvin scale, converting temperature to another is easy. You simply add subtract 273, as shown in the following equivalent from one or equations. Units of Energy Energy is the capacity to do work or to produce heat. The joule and the calorie are common units of energy. The joule (J) is the SI unit of energy.

5 One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1 C. 3.3 Conversion Factors A conversion factor is a ratio of equivalent measurements. The ratios 100 cm/1 m and 1 m/100 cm are examples of conversion factors. Conversion Factors When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same. Conversion Factors The scale of the micrograph is in nanometers. Using the relationship 10 9 nm = 1 m, you can write the following conversion factors. Dimensional Analysis Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements. Dimensional analysis provides you with an alternative

6 Converting Between Units Converting Between Units Converting Complex Units Many common measurements are expressed as a ratio of two units. If you use dimensional analysis, converting these complex units is just as easy as converting single units. It will just take multiple steps to arrive at an answer.

7 3.4 Density If you think that these lily pads float because they are lightweight, you are only partially correct. The ratio of the mass of an object to its volume can be used to determine whether an object floats or sinks in water. Determining Density Density is the ratio of the mass of an object to its volume. Determining Density Each of these 10-g samples has a different volume because the densities vary. Determining Density The density of corn oil is less than the density of corn syrup. For that reason, the oil floats on top of the syrup. Density and Temperature Experiments show that the volume of most substances increases as the temperature increases. Meanwhile, the mass remains the same. Thus, the density must change. The density of a substance generally decreases as its temperature increases.

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