Measurement Making measurements with Accuracy and Precision

When and why are significant figures used? 1. Sig figs are only used in measurements. 2. Sig figs are used to indicate the accuracy of a measurement. 3. They determine the accuracy of a value calculated from measurements.

Write the following question in your notebook/notes adding onto Fridays: What is the relationship between the measuring device being used and the number of significant digits that should be reported?

*A proper measurement should always go one more place value than the finest divisions (hashmarks) marked on the instrument. *Always estimate your last digit. Do not round off to the nearest hashmark.

Reporting Measurements  Using significant figures  Report what is known with certainty  Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Measuring Volume use mL milliliters, Graduated cylinder 1 L = 1000 mL 1 qt = 946 mL Timberlake, Chemistry 7 th Edition, page 3

Reading a Meniscus line of sight too high reading too low reading too high line of sight too low proper line of sight reading correct graduated cylinder 10 mL

20 10 ? 15 mL ? 15.0 mL1.50 x 10 1 mL

InstrumentHash marksPlace of certainty Place of estimation 10 ml graduated cylinder 100 ml graduated cylinder ruler Electronic balance Thermometer Create this table in your notebook.

Graduated cylinder Syringe Volumetric flask Buret Pipet Instruments for Measuring Volume

Counting Significant Figures The rules boil down to this…… When counting significant figures- Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson

Rules for counting sig figs 1. All non-zero numbers are significant Sandwiched zeros are significant Trailing zeros with decimal are significant Trailing zeros WITHOUT decimal are NOT significant Leading zeros NOT significant

Exact numbers (no doubt or uncertainty in the value) may be thought of as having an infinite number of significant digits. counted values I have 4 apples – no more- no less This also includes numbers that are defined values such as conversion factors. There are 100 centimeters in a meter 100 cm/1 m

Sig figs with scientific notation For Scientific notation just look at the first part and determine how many sig figs there are. Do not worry about the x 10 3 part

Rounding Rules If the digit following the last digit to be retained is..  Greater than 5, then increase by 1  Less than 5, then stay the same  5, then increase by 1

Significant Figures Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF Courtesy Christy Johannesson

Significant Figures Calculating with Sig Figs Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer mL mL 7.85 mL 224 g g 354 g  7.9 mL  350 g 3.75 mL mL 7.85 mL 224 g g 354 g Courtesy Christy Johannesson

Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g g g g 4 SF2 SF  2.4 g/mL 2 SF Courtesy Christy Johannesson

Scientific Notation: Powers of Ten Rules for writing numbers in scientific notation: 1. Write all significant figures but only the significant figures. 2. Place the decimal point after the first digit, making the number have a value between 1 and 10. Exponents of 10 a) Positive exponents The number becomes larger. It is multiplied by the power of 10. b) Negative exponents The number becomes smaller. It is divided by the power of 10. c) 10 o = 1 Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!a view from outer space to the inside of an atom

Scientific Notation Converting into scientific notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent 65,000 kg  6.5 × 10 4 kg Courtesy Christy Johannesson

Scientific Notation 7. 2,400,000  g kg 9.7  km  10 4 mm Practice Problems 2.4  10 6  g 2.56  kg km 62,000 mm Courtesy Christy Johannesson

Scientific Notation Calculating with scientific notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EE ÷ ÷ ENTER = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator: Courtesy Christy Johannesson

SIGNIFICANT FIGURES practice How many significant figures in the following numbers? 1) ) ) ) )Subtract = 6)Multiply 5.02 x = 7)Convert 5,200,000 to scientific notation 8)(6.2 x ) x (4.41 x 10 7 ) =

Le Systeme International d’Unites SI – system adopted in 1960 Seven base units, most others are derived from these seven. Defined in terms of standards of measurement, easy to preserve, reproduce and practical in size. See page 34 in book Style conventions – internationally seventy-five thousand written not 75,000

SI Units – standards of measurements Length Mass Time Temperature Amount of substance Electric current meters m kilograms kg seconds s Kelvin K moles mol Ampere A

SI Prefixes kilo-1000 deci- 1 / 10 centi- 1 / 100 milli- 1 / 1000 Also know… 1 mL = 1 cm 3 and 1 L = 1 dm 3

Factor Name Symbol Factor Name Symbol decimeter dm 10 1 decameter dam centimeter cm 10 2 hectometer hm millimeter mm 10 3 kilometer km micrometer  m 10 6 megameter Mm nanometer nm 10 9 gigameter Gm picometer pm terameter Tm femtometer fm petameter Pm attometer am exameter Em zeptometer zm zettameter Zm yoctometer ym yottameter Ym

Mass A measure of the amount of matter Mass is determined by comparing the mass of an object with a set of standard masses that are part of a balance What is the difference between mass and weight? Weight is the measure of the gravitational pull on matter ---Weight is measured on a spring scale. Page 35

Spring Scale – Uses Force of gravity to measure weight (grams or Newtons)

Volume Amount of space occupied by an object The derived SI Units for volume is cubic meters m 3 This large unit is inconvenient so instead cubic centimeter is used cm 3 Chemists often use a non-SI unit the Liter 1 L = 1 dm 3 = 1000 cm 3 So …… 1mL = 1 cm 3

Use combinations of SI units to get derived units For example: Area = length x width = m 2 Volume = length x width x height= m 3 Density = mass/volume Density units = g/cm 3 or g/mL or for gases g/L

Density Ratio of mass to volume D = mass/volume Physical property Doesn’t depend on size (intensive) Does depend on temperature. Why? Can be used to help identify a substance

Measurements Metric (SI) units Prefixes Uncertainty Significant figures Significant figures Conversion factors Conversion factors Length Density Mass Volume Problem solving with conversion factors Problem solving with conversion factors Timberlake, Chemistry 7 th Edition, page 40