Student can express numbers in scientific notation and apply significant figure rules in calculations.
Introduce scientific notation.
Chemistry involves atoms with extremely small masses and incredibly large numbers. To avoid writing endless zeros, chemists use scientific notation, also known as exponential notation.
A comparison table of precision vs accuracy helps clarify the difference.

This infographic illustrates the critical difference between precision and accuracy in scientific measurement using a target True Value of 2.00 g.
Accuracy: How close a measurement (or average of measurements) is to the true or accepted value. Precision (Consistency): How close a set of measurements are to each other.
High Precision, High Accuracy (Student C): Measurements (2.01 g, 1.99 g) are clustered tightly together and centered around the true value line.
High Precision, Low Accuracy (Student A): Measurements (1.95 g, 1.93 g) are clustered tightly together (consistent), but are far from the true value.
Low Precision, Low Accuracy (Student B): Measurements (1.94 g, 2.05 g) are scattered widely and do not align with each other or the true value.
Source examples of arithmetic with scientific notation.
Problem 1: Multiplication Multiply
Define precision, accuracy, and the rules of sig figs.
While analyzing data, we look at two qualities of our measurements:
Show how to round in addition vs multiplication.
Problem 1: Addition and Subtraction Add to the correct number of significant figures.
Practice applying significant figure rules to operations.
Let's apply the rules of significant figures to mathematical operations.
First, consider the addition of the numbers , , and . The unrounded sum is . Because has only one digit after the decimal point, the final result must also be limited to one decimal place, making it .
Next, let us calculate the product of and . The exact mathematical product is .
In multiplication, the result must be reported with no more significant figures than the measurement with the fewest significant figures. Since has two significant figures, we must round our product to two significant figures, resulting in .
Test sig fig counting from Exercise 1.19.
How many significant figures are present in the measurement ?