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Significant Figures and Precision in Scientific Measurements, Summaries of Mathematics

The concepts of significant figures, accuracy, and precision in scientific measurements. It covers the difference between accuracy and precision, the importance of equipment and technique in measurement, and methods for calculating percent error and precision. Examples and practice problems are provided.

What you will learn

  • What is the difference between accuracy and precision in scientific measurements?
  • How does the equipment used in a measurement affect its precision?
  • How can you determine if a set of measurements is precise?
  • What is percent error and how is it calculated?
  • What are the rules for using scientific notation?

Typology: Summaries

2021/2022

Uploaded on 09/27/2022

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Scientific Measurement
Significant Figures
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Scientific Measurement

Significant Figures

Accuracy vs. Precision

  • The Difference between Precision and Accuracy
  • Accuracy – the closeness of measurements to the correct or accepted value
  • How close to the target?
  • Precision – the closeness of a set of measurements of the same quantity made in the same way
  • How repeatable was the measurement?

Example 1

Standard electronic lab balance

  • trustworthy to the nearest milligram (0.001 g)

Example 2

Cheap balance

  • Measurements are trustworthy to the nearest gram

Practice Problem

  • A student measures the mass and the volume of a substance and calculates its density as 1.40g/mL. The correct, or accepted value of the density is 1.36g/mL. What is the percent error of the student’s measurement?

Answer

  • Data Set #
    • 3.06 – 3.02 =.
      • PRECISE!
    • 7.65 – 7.43 =.
      • NOT PRECISE!

Scientific Notation

  • A simple way to show large and small numbers
  • 300,000,000 = 3.0 x 10 8
  • .000034 = 3.4 x 10

  • Only one number should be to the left of the decimal - This is wrong 34.0 x 10 -

Scientific Notation

  • 1.234 x 10 5
  • 1.009 x 10

Scientific Notation

  • When adding and subtracting in scientific notation the exponent has to be equal
  • (4.215 x 10

     ) + (3.2 x 10 - ) 
  • When multiplying, multiply the numbers then add the exponents
  • (3.4 x 10 6 )(4.2 x 10 3 )
  • When dividing, divide the numbers then subtract the exponents
  • (3.2 x 10 3 )/(5.7 x 10 - )