Significant Figures and Precision in Scientific Measurements, Summaries of Mathematics

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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 - )