# Measurements and Calculations Chapter 2. Objectives Construct and use tables and graphs to interpret data sets. Solve simple algebraic expressions. Measure.

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Measurements and Calculations Chapter 2

Objectives Construct and use tables and graphs to interpret data sets. Solve simple algebraic expressions. Measure with accuracy and precision (length, volume, mass, temperature, time, etc.) Convert within a unit (such as, centimeters to meters). Use common prefixes such as milli-, centi-, and kilo-. Use scientific notation, where appropriate. Use ratio and proportion in the solution of problems.

Objectives Determine the correct number of significant figures. Determine percent error from experimental and accepted values. Use appropriate metric/standard international (SI) units of measurement for mass (kg); length (m); and time (s). Use Celsius and Kelvin scales.

Counting Significant Figures 1.All non-zero digits are significant –1.5 has 2 sig. figs. 2.Interior zeros are significant –1.05 has 3 sig. figs. 3.Leading zeros are NOT significant –0.001050 has 4 sig. figs. Presentation of Lecture Outlines, 1–4 Tro: Chemistry: A Molecular Approach, 2/e

Counting Significant Figures 4.Trailing zeros may or may not be significant a)Trailing zeros after a decimal point are significant 1.050 has 4 sig. figs. b)Trailing zeros before a decimal point are significant if the decimal point is written 150.0 has 4 sig. figs. c)Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation if 150 has 2 sig. figs. then 1.5 x 10 2 but if 150 has 3 sig. figs. then 1.50 x 10 2 Presentation of Lecture Outlines, 1–5 Tro: Chemistry: A Molecular Approach, 2/e

Significant Figures and Exact Numbers A number whose value is known with complete certainty is exact –from counting individual objects –from definitions 1 cm is exactly equal to 0.01 m –from integer values in equations in the equation for the radius of a circle, the 2 is exact Presentation of Lecture Outlines, 1–6 Exact numbers have an unlimited number of significant figures Tro: Chemistry: A Molecular Approach, 2/e

Example 1.5: Determining the Number of Significant Figures in a Number Presentation of Lecture Outlines, 1–7 How many significant figures are in each of the following? 0.04450 m 5.0003 km 10 dm = 1 m 1.000 × 10 5 s 0.00002 mm 10,000 m 4 sig. figs.; the digits 4 and 5, and the trailing 0 5 sig. figs.; the digits 5 and 3, and the interior 0’s infinite number of sig. figs., exact numbers 4 sig. figs.; the digit 1, and the trailing 0’s 1 sig. figs.; the digit 2, not the leading 0’s Ambiguous, generally assume 1 sig. fig. Tro: Chemistry: A Molecular Approach, 2/e

Study Buddy Review: Identify S.F. 1.523.1 mL 2.0.0025 mg 3.5002 km 4.1.8 x 10 6 lbs. 5.0.090180 L 6.2000 dogs 7.2010. cats 8.14,000.00 carrots

Study Buddy Review: Identify S.F. 1.523.1 mL4 2.0.0025 mg2 3.5002 km4 4.1.8 x 10 6 lbs.2 5.0.090180 L5 6.2000 dogs1 7.2010. cats4 8.14,000.00 carrots7

Multiplication and Division with Significant Figures When multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the lowest number of significant figures 5.02 × 89.665 × 0.10 = 45.0118 = 45 3 sig. figs. 5 sig. figs. 2 sig. figs. 2 sig. figs. 5.892 ÷6.10= 0.96590 = 0.966 4 sig. figs. 3 sig. figs. 3 sig. figs. Presentation of Lecture Outlines, 1–10 Tro: Chemistry: A Molecular Approach, 2/e

Addition and Subtraction with Significant Figures When adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the lowest number of decimal places Presentation of Lecture Outlines, 1–11 Tro: Chemistry: A Molecular Approach, 2/e

Study Buddy Review: S.F. in Calculations 1.Perform the following calculations and express your answer to the correct number of significant digits: a.1.27 / 5.296 cm 3 b.12.2 g + 0.38 g c.17.3 g + 2.785 g 30.20 cm 3

Study Buddy Review: S.F. in Calculations 1.Perform the following calculations and express your answer to the correct number of significant digits: a.1.27 / 5.296 cm 3 0.239 g/cm 3 b.12.2 g + 0.38 g12.6 g c.17.3 g + 2.785 g0.665 g/cm 3 30.20 cm 3

Rounding When rounding to the correct number of significant figures, if the number after the place of the last significant figure is a)0 to 4, round down –drop all digits after the last sig. fig. and leave the last sig. fig. alone –add insignificant zeros to keep the value if necessary b)5 to 9, round up –drop all digits after the last sig. fig. and increase the last sig. fig. by one –add insignificant zeros to keep the value if necessary To avoid accumulating extra error from rounding, round only at the end, keeping track of the last sig. fig. for intermediate calculations Presentation of Lecture Outlines, 1–14 Tro: Chemistry: A Molecular Approach, 2/e

Rounding Rounding to 2 significant figures 2.34 rounds to? 2.3 2.37 rounds to? 2.4 2.349865 rounds to? 2.3 Presentation of Lecture Outlines, 1–15 Tro: Chemistry: A Molecular Approach, 2/e

Scientific Notation: Writing Large and Small Numbers Move the decimal point to obtain a number between 1 and 10. ( If there is no decimal you may have to add one like below ) Multiply that number (the decimal part) by 10 raised to the power that reflects the movement of the decimal point. If the decimal point is moved to the left, the exponent is positive. If the decimal is moved to the right, the exponent is negative.

Convert 61300000 to scientific notation

Convert 0.000345 to scientific notation

Convert 5.8 x 10 5 to standard notation

Convert 2.07 x 10 -4 to standard notation

Study Buddy Review Convert the following to scientific notation: 0.005 g 10,000 m Convert the following to standard notation: 1.5 x 10 -3 dL 2.2 x 10 5 mL

Study Buddy Review Convert the following to scientific notation: 0.005 g5 x 10 -3 g 10,000 m1 x 10 4 m Convert the following to standard notation: 1.5 x 10 -3 dL0.0015 dL 2.2 x 10 5 mL220,000 mL

You are 100% responsible for knowing how to work your calculator 23 EXP EE X 10 n

The Metric System

Metric and SI units Metric System used in science SI System – International System of units based on metric system –Used to standardize quantities between scientists

Common Units in Chemistry Quantity it represents SI unitCommon metric unit in Chemistry Lengthmeter (m)centimeter (cm) Masskilogram (kg)gram (g) Volumem 3 (cubic meters) milliliter (mL) Temperature Kelvin (K)Celsius ( o C)

Common Decimal Prefixes Used with SI Units

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