Measurements

Units of Measurement

  • Every measurement has a known value and an estimated value.

    • Known values include all certain digits and one uncertain digit.

    • Always include one measurement number past the main graduation of the measuring device.

    • This practice ensures proper communication of types of measuring devices used.

Measurement Practice

  • Examples of items to measure:

    • Block

    • Black box

Digital Measurements

  • With electronic balances, the last digit fluctuates slightly and is considered estimated.

    • e.g., if the readout fluctuates between 3.44 and 3.45, one must decide if it’s closer to 4 or 5.

Types of Measurements

Measurement Components

  • Measurement can be analyzed:

    • Known: 24 km, 3.21 cm, 0.002545 g

    • Estimated: last digit in each measurement.

    • Units: important for clarity in communication.

SI Units

  • Common SI base units:

    • Length: meter (m)

    • Mass: kilogram (kg)

    • Time: second (s)

    • Temperature: Kelvin (K)

    • Amount of substance: mole (mol)

SI Prefixes

  • Large value prefixes:

    • tera (T): 10¹²

    • giga (G): 10⁹

    • mega (M): 10⁶

    • kilo (k): 10³

  • Small value prefixes:

    • centi (c): 10⁻²

    • milli (m): 10⁻³

    • micro (μ): 10⁻⁶

    • nano (n): 10⁻⁹

Mass vs. Weight

  • Mass: Measure of the amount of matter (grams, g or kilograms, kg).

  • Weight: Gravitational pull on mass.

  • Objects can be weightless but not massless.

Volume

  • Measurement of space occupied.

  • Units of volume can include:

    • milliliters (mL)

    • liters (L)

    • cubic centimeters (cm³)

    • cubic meters (m³)

  • Conversions: 1 mL = 1 cm³ = 1 cc.

Scientific Notation

  • Written as $x imes 10^n$ or with E notation (e.g., 6.02E23).

  • Positive exponent: Move decimal right for large numbers.

    • Example: 2.9979 × 10⁸ m/s = 299,790,000 m/s.

  • Negative exponent: Move decimal left for small numbers.

    • Example: 6.55 × 10⁻⁷ m = 0.000000655 m.

Significant Figures

  • Accuracy: Closeness to the correct value.

  • Precision: Reproducibility of measurements.

  • All measurements have some uncertainty.

Factors Affecting Measurement Reliability

  • Skill of measurer

  • Conditions of measurement

  • Quality of measuring instrument.

  • Significant figures method: Reflects all digits captured by measuring device.

  • All measured digits plus one estimated digit are significant.

Rules for Significant Figures

  1. All nonzero digits are significant.

  2. Zeros between significant digits are significant (trapped zeros).

  3. Leading zeros are not significant.

  4. Trailing zeros (after decimal) are significant.

  5. Trailing zeros without a decimal point are not significant.

  6. Conversion factors and counted numbers have unlimited significance.

Percent Error

  • Formula: ext{Percent Error} = 100 imes rac{ ext{Accepted Value} - ext{Experimental Value}}{ ext{Accepted Value}}

  • Lower percent error indicates higher accuracy.

    • Example: Accepted mass = 25.0 g, Experimental mass = 22.3 g.

Density

  • Defined as mass per unit volume.

  • Generally decreases with increasing temperature due to increased volume.

  • Density Formula: ext{Density} = rac{ ext{Mass}}{ ext{Volume}}

Factor Label Method

  • A conversion factor is a ratio from the equality between two different units.

  • Steps for using Factor Label:

    1. Start with known values; fewest units preferred.

    2. Use conversion factors to cross-cancel.

    3. Continue adding conversions until the correct unit remains.

    4. Execute the necessary calculations.

Conversion Examples

  1. Convert 54 inches to feet (1 ft = 12 in).

  2. Convert 1.3 miles to inches (5280 ft = 1 mi).

  3. Convert 1.3 × 10²⁰ cm to miles (2.54 cm = 1 in).

  4. Convert grams of water to molecules (18.02 g = 1 mol, 6.02E23 molecules = 1 mol).