Scientific Measurement

• Measurement


  A quantitative comparison of an object's physical quantity that involves a number and a unit
• Unit


  The magnitude of a physical quantity and may vary as a standard or non-standard unit
• Metric System


  • Based upon the power of ten to express a very large or very small number
• Base Units

  • Meter - length
  • Gram - mass
  • Liter - volume
• SI (Systeme International) unit


  • Based on the metric system but has 7 fundamental units
  • Each prefix of the International System of units denotes a decimal number in a measurement expressed in the power of ten
  • For example, in mg; milli is the prefix used to denote the magnitude of the unit and gram is the base unit
• 7 SI Fundamental Units

  • Mass: Gram: g
  • Electric Current: Ampere: A
  • Temperature: Kelvin: K
  • Time: Second: s
  • Amount of Substance: Mole: mol
  • Length: Meter: m
  • Luminous Intensity: Candela: CD
• Scientific Notation


  A simplified expression for a very large or very small number or quantity
• Standard form of scientific notation

  A x 10^b
• Expressing LARGE Numbers in Scientific Notation

  1. Move the decimal point to the LEFT

  2. The number of times the decimal point is moved indicates the decrease or increase in the exponent

  3. The exponent is positive when expressing large numbers
• Expressing SMALL Numbers in Scientific Notation

  1. Move the decimal point to the RIGHT

  2. The exponent is negative when expressing smaller numbers
• Conversion Factor


  • A mathematical statement of two equivalent measurements of different units that can be expressed in fraction form
  • Ratio which represents the relationship between two units
  • Always equal to one
• Accurate


  Capable of providing a correct reading or measurement
• Accuracy


  • A measure of how close a measurement comes to the actual or true value of what's being measured
  • How close you are to the accepted value
• Precision


  • The degree of consistency and agreement among independent measurements of the same quantity for the reliability of results
  • A measure of how close a series of measurement are to one another
  • How carefully measurements were made
  • If the true value is not given, get the average of the series of measurements then compare
• Determining Error

  Error = Ev - Av
• Experimental value (ev)


  Is measured in the lab
• Accepted Value (av)


  Is the correct or true value based on reliable references
• Error


  Is the difference between the ev and av
• Percent Error


  • Percent Error = (Ev- Av) / Av (100)
  • The percent error is an absolute value (no positive/ negative)
• The acceptable percent of error is +/- 5%
• Significant Figures


  • Each of the digits of a number that are used to express it to the required degree of accuracy and precision
  • Digits that convey precision with which a number is known
• Rules in Determining Significant Figures

  • All nonzeroes are significant
  • Zeroes between nonzeroes are significant
  • Leading zeroes (zeroes from the left of a nonzero) are not significant
  • Trailing zeroes (zeroes after the nonzero) are significant
  • Every digit in a scientific notation is significant
  • Final Zeroes may or may not be significant - significant if behind a decimal point, otherwise if after a decimal point, drawing a bar on top of the zeroes could make it significant
• Rounding-off Numbers


  A value is raised or lowered to a much more precise number
• Rounding Rules

  • If the digit is greater than 5, add one then drop all the digits
  • If the digit to be dropped is less than 5, drop it without adding anything
  • If the digit is exactly 5 and the digit to be retained (left of 5) is even, then just drop the 5
  • If the digit to be retained is odd, then add one and drop
• Addition and Subtraction


  1. The number of decimal places in the final answer should be equal to the smallest number of decimal places

  2. The answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places
• Multiplication and Division


  1. The significant figures and not the decimal places

  2. The final answer cannot contain more significant figures than those in the least accurate measurement
• Mixed Operations


  1. When multiple operations are used, evaluate the ones inside the parenthesis then round it to the number of significant figures

  2. Use the rounded number to proceed to the next operation