Uncertainty in MeasurementAccuracy, Precision, Error and Significant Figures

Objectives Define and compare accuracy

and precision.

Describe the accuracy of experimental data using error and percent error.

Apply rules for significant figures to express uncertainty in measured and calculated values.

Accuracy and Precision

Accuracy refers to how close a measured value is to an accepted value.

Precision refers to how close a series of measurements are to one another.

Accurate or Precise?

Accurate or Precise?

Accurate or Precise?

Accurate or Precise?

Significant FiguresPrecision is limited by the tools

available.Significant figures are the

numbers of digits obtained from a measurement.

The significant figures include all known digits plus one estimated digit.

Rules for Determining the Number of Significant Figures

1. Numbers that are not zero are significant.

2. A zero in between two nonzero digits is significant.

3. If a number has a decimal point, all zeroes after a nonzero digit are significant.

4. If there is no decimal point, zeroes on the right hand side are not significant.

Counting Significant Figures500

5.404

305

4.000

0.0340

Easy Method

Pacific Ocean

Atlantic Ocean

If decimal is Present, count from left to right.

If decimal is Absent, count from right to left.

In both cases, begin counting with the first nonzero digit you encounter.

Counting Significant Figures400

4.20

305

6.907

0.0780

Calculations with Significant FiguresAddition and subtraction

◦Determine which number has the fewest decimal places.

◦Round answer to that number of decimal places.

◦6.02 + 3.1 = ?

◦8.99 - 5.333 = ?

Calculations with Significant FiguresMultiplication and division

◦Answer has same significant digits as the measurement with least significant digits.

◦9.99 / 3 = ?

◦9.99 / 3.0 = ?

Calculations with Significant FiguresMain Idea

◦When rounding an answer after a calculation, the final answer should match the given information in terms of total digits.

◦If you multiply two 2-digit numbers, the final answer should also have two digits.

ErrorError is defined as the difference

between and experimental value and an accepted value.

The error equation is error = experimental value – accepted value.

Percent ErrorPercent error expresses error

as a percentage of the accepted value.