Units of Measurements

Physical Quantities and SI Units

  • Physical quantities in the International System of Units (SI) are expressed using seven fundamental physical units

    • Units include length, mass, time, electric current, temperature, amount of a substance, and luminous intensity

  • Two major systems of units: SI units and English units

    • The United States is the only country extensively using English units

  • Seven fundamental physical quantities in physics: length, mass, time, electric current, temperature, amount of substance, and luminous intensity

  • SI Base Units: meter, kilogram, second, ampere, kelvin, mole, and candela

Metric Prefixes

  • Metric system includes prefixes based on factors of 10 for easy conversions

  • Metric Prefixes: Exa, Peta, Tera, Giga, Mega, Kilo, hecto, Deka, Deci, Centi, Milli, Micro, Nano, Pico, Femto, Atto

  • Advantages of the metric system: simple conversions by moving decimal place, sequential powers of 10, no need for new units for different scales

  • Metric system allows for easy conversions due to sequential powers of 10

  • Comparison of metric system with nonmetric systems like U.S. customary units

  • Metric system's advantage in using appropriate prefixes for large ranges of values

Common temperature scales

  • Three common temperature scales: Celsius, Fahrenheit, and Kelvin

  • Conversion formulas between Celsius, Fahrenheit, and Kelvin

  • Unit conversion using conversion factors and dimensional analysis

  • Scientific notation for writing large or small numbers conveniently

  • Scientific notation format: x * 10^y

  • Moving decimal point in scientific notation to represent large or small numbers

  • Indicating fractions in scientific notation with negative y value

  • Example of converting numbers to scientific notation for convenience

  • Differentiating Accuracy from Precision

    • Accuracy

      • Definition: Closeness of a measurement to the correct value

      • Example: Measuring paper length

      • Calibration importance for accuracy

    • Precision

      • Definition: Consistency of repeated measurements

      • Analyzing precision through range of measurements

      • Example: Printer paper measurements

  • Accuracy and Precision Relationship

    • Accuracy and precision in measurements

    • GPS system example for accuracy and precision illustration

  • Definition of Error

    • Error Types

      • Random error and systematic error

    • Random Error

      • Definition and characteristics

      • Examples of causes

    • Systematic Error

      • Definition and causes

      • Categorized into instrumental, environmental, and observational errors

  • Types of Systematic Errors

    • Instrumental Error

      • Reasons for occurrence

    • Environmental Error

      • Causes related to external conditions

    • Observational Error

      • Definition and significance in statistics

  • Systematic Errors

    • Reproducible inaccuracies in measurements

    • Difference from random errors

  • Measurement Error Scenarios

    • Examples of measurement errors: calibration, human, parallax, and systematic errors

  • Observation Error

    • Definition and relation to random error

    • Importance of multiple measurements for reducing observation error

  • Significant Figures in Measurement

    • Importance of honesty in reporting measurements

    • Significance of significant figures in accuracy

    • Rounding numbers for achieving significant figures

  • Significant Figures Calculation

    • Examples of calculations with correct significant figures

General

  • Measurement Concepts

    • Understanding accuracy, precision, errors, and significant figures in measurements

  • Error Reduction

    • Importance of calibration, multiple measurements, and understanding error types

  • Accuracy and Precision

    • Accuracy refers to how close a measured value is to the true value.

    • Precision refers to how close the measured values are to each other.

  • Random and Systematic Error

    • Random errors are unpredictable and can occur in any direction.

    • Systematic errors are consistent and repeatable, affecting all measurements in the same way.

  • Rules for Significant Figures

    • Non-zero numbers are significant.

      • Example: 33.2 has three significant figures.

    • Zeros between two non-zero digits are significant.

      • Example: 2051 has four significant figures.

    • Leading zeros are not significant.

      • Example: 0.54 has two significant figures.

    • Trailing zeros to the right of the decimal are significant.

      • Example: 92.00 has four significant figures.

  • Significance of Zeros

    • Zero denotes actual information and can be significant.

    • Trailing zeros in a whole number with the decimal shown are significant.

      • Example: "540." has three significant figures.

    • Trailing zeros in a whole number with no decimal shown are not significant.

      • Example: "540" has two significant figures.

    • Exact numbers have an infinite number of significant figures.

  • Scientific Notation

    • In scientific notation, all digits comprising N are significant.

    • Manipulating the form of a number can change the number of significant figures.

      • Example: 5.02 x 10^4 has three significant figures.

  • Determining Significant Figures

    • Rules for determining significant figures:

      1. Non-zero digits are always significant.

      2. Zeros between two significant digits are significant.

      3. Final zero or trailing zeros in the decimal portion only are significant.

    • For addition and subtraction, the final answer's significant figures are limited by the least number of significant figures in the problem.

    • For multiplication and division, the least number of significant figures in any number of the problem determines the number of significant figures in the answer.