Review of Metric System, Precision and Accuracy, and Significant Figures

Chapter Overview

• Sections 1.7: Metric System, Precision and Accuracy, Significant Figures

• Sections 1.8: Unit Conversions and Dimensional Analysis

Metric System

• The Metric System (SI - System International) is used extensively in science.

  • Common Units:

  • Length: meter (m)

  • Mass: kilogram (kg)

  • Time: second (s)

  • Temperature: kelvin (K)

  • Amount of substance: mole (mol)

    • 6.02 x 10^23 units

Prefix Multipliers

• Prefix multipliers are used to represent different scales in the metric system:

  • mega- (M): 1,000,000 (Base x 10^6)

  • kilo- (k): 1,000 (Base x 10^3)

  • deci- (d): 0.1 (Base x 10^-1)

  • centi- (c): 0.01 (Base x 10^-2)

  • milli- (m): 0.001 (Base x 10^-3)

  • micro- (μ): 0.000001 (Base x 10^-6)

  • nano- (n): 0.000000001 (Base x 10^-9)

  • pico (p): 0.000000000001 (Base x 10^-12)

Temperature Scales

• Common Scales:

  • Fahrenheit (°F)

  • Celsius (°C)

  • Kelvin (K):

  • 
    K = °C + 273.15

  • 1 degree Celsius = 1 Kelvin

  • °C = \frac{5}{9}(°F - 32)

    • The size of degrees Celsius and Fahrenheit is different.

Measurements

• Uncertainty in Measurements:

  • Present in all measured values, necessitating the use of significant figures.

  • More significant figures indicate greater reliability (precision) of the measurement.

Significant Figures

• Importance:

  • Confidence in the reliability of measured values depends on significant figures.

• Rules:

  • Nonzero numbers are always significant.

  • Zeros between significant figures are significant.

  • Leading zeros are not significant.

  • Trailing zeros are significant only with a decimal present.

  • E.g. 0.0592 has 3 sig figs, 101.3 has 4 sig figs.

Calculations with Significant Figures

• Addition/Subtraction:

  • Result should have the same number of decimal places as the least precise measurement.

  • E.g., 2.45 + 4.1 has 1 decimal place in result.

• Multiplication/Division:

  • Result should have the same number of significant figures as the least precise measurement.

• Counting Numbers:

  • Defined quantities (like 1 meter = 100 cm) have infinite significant figures.

Rounding Rules

• When Rounding:

  • If the first dropped digit is less than 5, do not change the number.

  • If it's 5 or more, round up.

• E.g. 5.37 rounds to 5.4; 5.34 rounds to 5.3.

Density Calculations

• Definition:

  • Density is mass per unit volume.

• Formula:

  • D = \frac{M}{V}

  • Units: g/cm³ or g/mL

• Example: If mass = 35g and volume = 7cm³,

  • D = \frac{35 g}{7 cm³} = 5 g/cm³

Dimensional Analysis

• Definition:

  • Approach used in solving chemistry problems, primarily for unit conversion.

• Conversion Factors:

  • Ratios representing equivalent quantities (e.g., 1 in = 2.54 cm).

• Procedure:

  • Use conversion factors to cancel initial units and establish desired units.

Units Raised to a Power

• When converting units raised to a power, ensure both the number and unit are raised.

• E.g. converting cm³ to m³, involve the factor:

  • 1 m³ = 1,000,000 cm³

Precision vs. Accuracy

• Precision:

  • Reflects reproducibility of measurements (agreement between values).

• Accuracy:

  • Closeness of a measurement to the true value.

• Metrics:

  • Precision can be expressed using range or standard deviation; accuracy often considered as error in measurement.