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Lesson 1.5: Uncertainty in Measurement

← Lesson 1.4: Lesson 1.6: →

Example 1: How would you record the length of the red line? How many significant figures does the measurement contain?

Example 2: How would you record the length of the red line? How many significant figures does the measurement contain?

Example 3: How would you record the length of the red line? How many significant figures does the measurement contain?

Example 4: How would you record the volume of the liquid used? How many significant figures does the measurement contain?

Example 5: How many significant figures are in the following?

Significant Figures in Calculations

There are two rules, one for multiplication and another for addition. Focus on the rule for multiplication – this is what we use most of the time.

The rule for multiplication

The result of your calculation should be no more precise than the measurement with the least number of significant figures.

Example 6: What is the density of an object that has a mass of 2.46 g and a volume of 2.0 ml?

$$ \begin{align*} density &= \frac{mass}{volume}\\\\ density &= \frac{2.46 \, g}{2.0 \, ml} \\\\ & = 1.23 \, g/ml \\\\ & = 1.2 \, g/ml \end{align*} $$

Example 7: What is the average velocity of an object that covers 125.0 m in 3.2 s?

$$ \begin{align*} velocity &= \frac{distance}{time}\\\\ velocity &= \frac{125.0 \, m}{3.2 \, s} \\\\ & = 39.0625 \, m/s \\\\ & = 39 \, m/s \end{align*} $$

Example 8: What is the density of an object that has a mass of 0.124 g and a volume of 0.100 cm3?

$$ \begin{align*} density &= \frac{mass}{volume}\\\\ density &= \frac{0.124 \, g}{0.100 \, cm^3} \\\\ & = 1.24 \, g/cm^3 \end{align*} $$

The rule for addition

The result of your calculation should have the same number of decimal places as the least precise measurement.

Example 9: What is the sum of three measures made with different rulers: 12.44 cm + 1.686 cm + 15.1 cm?