Solve Apply the concepts to this problem. Sample Problem 3.5 Solve Apply the concepts to this problem. Align the decimal points and add the numbers. a. 12.52 meters 349.0 meters + 8.24 meters 369.76 meters 2

Solve Apply the concepts to this problem. Sample Problem 3.5 Solve Apply the concepts to this problem. a. 12.52 meters 349.0 meters + 8.24 meters 369.76 meters 2 369.8 meters = 3.698 x 102

Solve Apply the concepts to this problem. Sample Problem 3.5 Solve Apply the concepts to this problem. Align the decimal points and subtract the numbers. b. 74.636 meters - 28.34 meters 46.286 meters 2

Solve Apply the concepts to this problem. Sample Problem 3.5 Solve Apply the concepts to this problem. b. 74.636 meters - 28.34 meters 46.286 meters 2 = 46.29 meters = 4.629 x 101 meters

Multiplication and Division 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.

Significant Figures in Multiplication and Division Sample Problem 3.6 Significant Figures in Multiplication and Division a. 7.55 meters x 0.34 meter b. 2.10 meters x 0.70 meter c. 2.4526 meters2 ÷ 8.4 meters d. 0.365 meter2 ÷ 0.0200 meter

Answers a. 7.55 meters x 0.34 meter = 2.567 meters2 = 2.6 meters2 b. 2.10 meters x 0.70 meter = 1.47 meters2 = 1.5 meters2 c. 2.4526 meters2 ÷ 8.4 meters = 0.291 076 meter = 0.29 meter d. 0.365 meters2 ÷ 0.0200 meter = 18.25 meters = 18.3 meters

In what case are zeros not significant in a measured value?

In what case are zeros not significant in a measured value? Sometimes zeros are not significant when they serve as placeholders to show the magnitude of the measurement.

Key Concepts In scientific notation, the coefficient is always a number greater than or equal to one and less than ten. The exponent is an integer. To evaluate accuracy, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated 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.

Key Equations Error = experimental value – accepted value Percent error = |error | ____________

Glossary Terms measurement: a quantitative description that includes both a number and a unit scientific notation: an expression of numbers in the form m x 10n, where m is equal to or greater than 1 and less than 10, and n is an integer accuracy: the closeness of a measurement to the true value of what is being measured precision: describes the closeness, or reproducibility, of a set of measurements taken under the same conditions

Glossary Terms accepted value: a quantity used by general agreement of the scientific community experimental value: a quantitative value measured during an experiment error: the difference between the accepted value and the experimental value percent error: the percent that a measured value differs from the accepted value significant figure: all the digits that can be known precisely in a measurement, plus a last estimated digit

BIG IDEA Scientists express the degree of uncertainty in their measurements and calculations by using significant figures. In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

MEASUREMENT

SI Units of Measurement 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

Commonly Used Metric Prefixes Symbol Meaning Factor mega M 1 million times larger than the unit it precedes 106 kilo k 1000 times larger than the unit it precedes 103 deci d 10 times smaller than the unit it precedes 10-1 centi c 100 times smaller than the unit it precedes 10-2 milli m 1000 times smaller than the unit it precedes 10-3 micro μ 1 million times smaller than the unit it precedes 10-6 nano n 1 billion times smaller than the unit it precedes 10-9 pico p 1 trillion times smaller than the unit it precedes 10-12

Metric Units of Mass Unit Symbol Relationship Example Kilogram (base unit) kg 1 kg = 103 g small textbook ≈ 1 kg Gram g 1 g = 10-3 kg dollar bill ≈ 1 g Milligram mg 103 mg = 1 g ten grains of salt ≈ 1 mg Microgram μg 106 μg = 1 g particle of baking powder ≈ 1 μg

Volume Metric Units of Volume Unit Symbol Relationship Example Liter L base unit quart of milk ≈ 1 L Milliliter mL 103 mL = 1 L 20 drops of water ≈ 1 mL Cubic centimeter cm3 1 cm3 = 1 mL cube of sugar ≈ 1 cm3 Microliter μL 103 μL = 1 L crystal of table salt ≈ 1 μL

Temperature Conversions K = °C + 273 °C = K – 273

Density The relationship between an object’s mass and its volume tells you whether it will float or sink. This relationship is called density. Density is the ratio of the mass of an object to its volume. mass volume Density =

Density When mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm3). The SI unit of density is kilograms per cubic meter (kg/m3). Density is an intensive property

Density This figure compares the density of four substances: lithium, water, aluminum, and lead. Increasing density (mass per unit volume) 10 g 0.53 g/cm3 19 cm3 10 cm3 3.7 cm3 0.88 cm3 1.0 g/cm3 2.7 g/cm3 0.88 g/cm3

Density Because of differences in density, liquids separate into layers. As shown at right, corn oil floats on top of water because it is less dense. Corn syrup sinks below water because it is more dense. Corn oil Water Corn syrup