Uncertainty in Measurement

Measurements are made in scientific laboratories, and are commonly used in scientific calculations. To carry out scientific calculations properly it is important to discuss the following concepts;

• Accuracy
  • refers to the agreement of a particular value with the true value.
• Precision
  • refers to the degree of agreement among several measurements of the same quantity.
  • Sample animation differentiating between accuracy and precision.
• Exact numbers
  • those numbers that we know exactly. Counting objects is an experiment that can be carried out with complete accuracy.
• Uncertainty
  • . numbers that are not known exactly. When we measure lengths (of an object), volumes (of a liquid) or masses (of a solid) the measurements are not exact, they have some degree of uncertainty.
• Sample animation demonstrating uncertainty in measurement.

Significant figures

• A useful method to express the uncertainty in measurement.
• Significant figure rules(see pages 20 and 21 in BLB)
  1. All nonzero digits are significant
  2. Zeros between nonzero digits are significant
  3. Zeros that precede the first nonzero digit are not significant. Reading from left to right begin counting with the first nonzero digit.
  4. Zeros are significant when they appear; in the middle of a number, at the end of a number that includes a decimal point.
  5. Zeros at the end of a number without a decimal point are ambiguous. We will assume they are NOT significant.

Practice assigning significant figures.

(Note: The Practicing assigning significant figures is a HyperCard stack. Inorder for this file to run you will have to have HyperCard installed on your computer. If you are on a PC you are OUT OF LUCK. If you are on a Mac there is a chance.)

Using Significant Figures (Practice animation )

• Addition and subtraction
  • When adding or subtracting measured quantities, there should be the same number of decimal places in the answer as there are in the measurement with the least number of decimal places. For addition and subtraction the number of significant figures is NOT important.
• Multiplications and Division
  • When multiplying and dividing measured quantities, there should be as many significant figures in the answer as there are in the measurement with the least number of significant figures.
• Rounding Rules

  Look at the left most digit to be dropped

  • If this digit is '5' or greater, or is '5' followed by nonzero digits, add '1' to the last digit to be retained and drop all the digits further to the right.
  • If this digit is less than '5', drop it and all digits further to the right.

Dimensional Analysis/Unit Conversions