1. Dealing with Uncertainty
Chapter 2, Unit C
Dealing with Uncertainty

2. Essential Question
How can we make sure we are looking at numbers with certainty, and know when things are not as clear as they appear to be?

3. Significant Digits

4. Practice Significant Digits & Implied Precision (17-28)
,000

5. Practice Rounding (15-16) Round to nearest whole number 3.49 5.299999
Round to the nearest tenth and ten

6. Accuracy & Precision Accuracy:
How closely a measurement approximates a true value
Accurate measurement has a small relative error
Precision:
Describes the amount of detail in a measurement

7. Example of Accuracy and Precision
Example: If your true weight is pounds. The scale at the doctor’s office (measures to the nearest pound) says you weigh 102 pounds. The scale at the gym (measures to the nearest 0.1 pound) says that you weigh pounds. Which scale is more precise? Which scale is more accurate?

8. Type of Errors
Random: occur because of random and inherently unpredictable events in the measurement process (ex: baby moving on a scale causes the scale readings to jump around randomly)
Systematic: occur when there is a problem in the measurement system that affects all measurements in the same way, such as making them all too low or too high by the same amount (ex: the scale measures 2.5 lbs. even when nothing is on the scale)

9. Size of Error (47-54) Absolute error = measured value – true value
Relative error = (measured value – true value)/(true value) x 100%

10. Example for Absolute & Relative Error
Doctor’s scale:
Absolute error = 102 – = -0.2
Relative error = ( )/(102.2)= (-0.2)/(102.2) = = -0.2%
Gym’s scale:
Absolute error = = -1.5
Relative error = (100.7 – 102.2)/(102.2)=
(-1.5)/(102.2)=-0.014= -1.4%