Dealing with Uncertainty Chapter 2, Unit C Dealing with Uncertainty

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?

Significant Digits

Practice Significant Digits & Implied Precision (17-28) 1.320 5.0 470 1,000 100.0 0.005 30330 0.00030

Practice Rounding (15-16) Round to nearest whole number 3.49 5.299999 3.49 5.299999 2899.5 4.01 0.33 -15.8 Round to the nearest tenth and ten 489.5 -54.82 98.76543 2.545 18.200001 -9.762

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

Example of Accuracy and Precision Example: If your true weight is 102.2 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 100.7 pounds. Which scale is more precise? Which scale is more accurate?

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)

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

Example for Absolute & Relative Error Doctor’s scale: Absolute error = 102 – 102.2 = -0.2 Relative error = (102-102.2)/(102.2)= (-0.2)/(102.2) = -0.002= -0.2% Gym’s scale: Absolute error = 100.7-102.2 = -1.5 Relative error = (100.7 – 102.2)/(102.2)= (-1.5)/(102.2)=-0.014= -1.4%