Measurements and Sig Figs Pt. 2

Introduction

  • Importance of treating numbers correctly in chemistry.

  • Measurements are taken in the lab using various instruments.

  • Questions involve how to record calculated answers accurately.

Example of Measurement

  • Situation: Determining fuel efficiency of a car.

  • Measurements: 278 miles driven, 11.70 gallons used.

  • Calculation: Fuel efficiency calculated as \frac{278}{11.70} gives approximately 23.7608.

  • Question arises: How to round the answer?

  • Concluded Answer: 23.8 miles per gallon.

Exact vs. Measured Numbers

  • Exact Numbers:

    • Examples: Counting items (12 eggs, 3 marbles).

    • Defined quantities (1,000 m in a kilometer).

    • Not measurements but definitions.

  • Measured Numbers:

    • Obtained by using instruments (e.g., balance, ruler).

    • Examples:

    • Balance measure: 126 lbs weight from Publix.

    • Pencil measure: 5.430 g.

    • Length measure: 10.54 cm.

Measuring Instruments

  • Common instruments in a lab include:

    • Graduated cylinders

    • Syringes

    • Pipets

    • Volumetric flasks

    • Rulers

  • Measurement scales can be:

    • Analog: Noticed visually (e.g., graduated cylinders).

    • Digital: Record every digit displayed (e.g., balance reads 1.102).

Reading a Graduated Cylinder

  • Proper measurement technique involves:

    • Observing the meniscus at eye level.

    • Reading the bottom of the meniscus between markings (4.5 and 4.6).

    • Estimate additional decimal for uncertainty.

  • Example Read: Estimated value could be 4.57 (with uncertainty).

  • Significance: Three measured numbers or significant figures recorded.

Definition of Significant Figures

  • Significant Figures: Measurements that include the uncertainty.

  • Example: Length recorded as 20 cm might have uncertainty of if it was closer to 21 or 22.

Rules for Determining Significant Figures

  • Non-zero digits: Always significant.

  • Zeros: Conditions determining significance include:

    • Sandwiched zeros between two significant figures are significant (e.g., 702).

    • A zero to the right of decimal and a non-zero digit is significant (e.g., for 20.0).

  • Trailing Zeros:

    • Zeros in whole numbers without decimal presence are not counted as significant (e.g., 200, 2,000 have one significant figure—2).

    • If exact, indicated by a decimal point, then considered significant (e.g., 20.0).

Decimal Places and Significant Figures

  • Trailing Zeros in decimals can show exact measures (e.g., 20.00 has four significant figures).

  • Learning Checks: Various provided numbers assessed for significant figures based on outlined rules.

Rounding Numbers

  • For calculations (addition/multiplication) rounding is based on significant figures:

    • When performing multiplication/division, round the answer to the least number of significant figures from the measurements used.

    • If calculated values extend beyond significant figures, round based on the following:

    • If the number after the chop point is less than five: drop the rest.

    • If it's five or greater, increase by one.

Rounding Examples

  1. For significant figures: 8,928 rounded to 8,900 with three significant figures.

  2. Defined cases of rounding: 145.50 rounded to 146.

Addition and Subtraction Rules

  • For addition/subtraction, round to the least number of decimal places:

    • Example: 9.463 to 3 decimal places and 3.2 to 1 decimal place results in an answer rounded to 12.7.