5 Steps to a 5 AP Chemistry 2019

Basics ‹ 47

The measurements used in calculations may contain varying numbers of significant

figures, so carry as many as possible until the end and then round off the final answer. The

least precise measurement will determine the significant figures reported in the final answer.

Determine the number of significant figures in each measured value (not the exact ones) and

then, depending on the mathematical operations involved, round off the final answer to

the correct number of significant figures. Here are the rules for determining the number of

significant figures in a measured value:

1. All non-zero digits (1, 2, 3, 4, etc.) are significant.

2. Zeroes between non-zero digits are significant.

3. Zeroes to the left of the first non-zero digit are not significant.

4. Zeroes to the right of the last non-zero digit are significant if there is a decimal point

present, but not significant if there is no decimal point.

Rule 4 is a convention that many of us use, but some teachers or books may use alternative

methods.

By these rules, 230,500. would contain 6 significant figures, but 230,500 would

contain only 4.

Another way to determine the number of significant figures in a number is to express

it in scientific (exponential) notation. The number of digits shown is the number of

significant figures. For example, 2.305 × 10 -^5 would contain 4 significant figures. You may

need to review exponential notation.

In determining the number of significant figures to be expressed in the final answer,

the following rules apply:

1. For addition and subtraction problems, the answer should be rounded off to the same

number of decimal places as the measurement with the fewest decimal places.

2. For multiplication and division problems, round off the answer to the same number of

significant figures in the measurement with the fewest significant figures.

Remember: Carry as many numbers as possible throughout the calculation and only round

off the final answer.

The use of an improper number of significant figures may lower your score on the

AP exam.

Dimensional Analysis—the Factor Label Method

Dimensional analysis, sometimes called the factor label (unit conversion) method, is a method

for setting up mathematical problems. Mathematical operations are conducted with the units

associated with the numbers, and these units are canceled until only the unit of the desired

answer is left. This results in a setup for the problem. Then the mathematical operations can

efficiently be conducted and the final answer calculated and rounded off to the correct number

of significant figures. For example, to determine the number of centimeters in 2.3 miles:

First, write down the initial data as a fraction:

2.3mi

1

Convert from miles to feet:

×

2.3mi

1

5,280ft

1mi

TIP

KEY IDEA

KEY IDEA