Review of Essential Skills:

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Presentation transcript:

Review of Essential Skills: Accuracy vs. Precision

Calculations Involving Measured Quantities The accuracy of a measured quantity is based on the measurement tool. The last digit always represents a guess. Rule: When making measurements, estimate your measure to the closest tenth of the smallest scale.

Consider a line of length 5.85 cm using the ruler below: The final digit of 5.85 cm is an estimate of the nearest tenth of the scale. Using our rounding rule >> 5.85 cm = 5.8 cm Therefore our answer is accurate to 2 sig figs where “.8” is the least reliable digit.

Accuracy vs. Precision Accuracy: The number of significant digits within a measured quantity. Precision: The smallest scale of the measurement represented by the last significant digit.

Eg.1: For each value below determine The number of significant figures The accuracy of the value The precision of the value Value I = 1.0890 cm y = 240 m z = 5.098 x 10-2 m a) b) c) 5 2 4 I accurate to 5 sig figs y accurate to 2 sig figs z accurate to 4 sig figs I precise to 10-4 cm y precise to 10 m z precise to 10-5 m

Operations & Measured Quantities Addition & Subtraction (precision-based) Answer is expressed with same precision of least precise quantity. Multiplication & Division (accuracy-based) Answer is expressed with same accuracy of least accurate quantity.

Eg. 2: Find the total volume for the following quantities: 95 mL, 3 Eg.2: Find the total volume for the following quantities: 95 mL, 3.27 mL and 2.10 mL Eg.3: Find the perimeter for the following scalene triangle: 137 cm, 2.1 m, 5 cm Eg.4: Add the following time intervals: 3.02 s, 4.5 s, 0.05h. Eg.5: Find the volume of the box with the following dimensions: l = 2.1 cm, w=2.01 cm, h = 1.09 cm