Lesson 2-3

Significant Digits or Figures

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    Significant digits, which are also called significant figures, are very important in Chemistry. Each recorded measurement has a certain number of significant digits. Calculations done on these measurements must follow the rules for significant digits. The significance of a digit has to do with whether it represents a true measurement or not. Any digit that is actually measured or estimated will be considered significant. Placeholders, or digits that have not been measured or estimated, are not considered significant. The rules for determining the significance of a digit will follow.

Rules For Significant Digits

1. Digits from 1-9 are always significant.
2. Zeros between two other significant digits are always significant
3. One or more additional zeros to the right of both the decimal place and another significant digit are significant.
4. Zeros used solely for spacing the decimal point (placeholders) are not significant.

    Recognizing significant digits will become much easier over time, as you continue to practice the rules.  Below are some examples, which show the number of significant digits in a group of numbers, and an explanation why the digits are significant.

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Alternate Rule for Significant Digits

Here is an alternate rule for determining significant digits that Mr. McNamara taught me last year.  He, in turn, learned it from a show on television.   If I could credit the person who made it up, I would.  The rule is really a "trick", which might allow students to get the correct answers without really understanding the concepts.  I would recommend that students only use this as a secondary method, for the purpose of checking their answers.

     When you look at the number in question, you must determine if it has a decimal point or not.  If it has a decimal, you should think of "P" for "Present".  If the number does not have a decimal place, you should think of "A" for "Absent".

Example, for  the number 35.700, think "P", because the decimal is present.

For the number 6500, you would think "A", because the decimal is absent.

     Now, the letters "A" and "P" also correspond to the "Atlantic" and "Pacific" Oceans, repectively.  Now, assume the top of the page is North, and imagine an arrow being drawn toward the number from the appropriate coast.  Once the arrow hits a nonzero digit, it and all of the digits after it are significant.

Let's look at one more example.

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Each number that we record as a measurement contains a certain number of significant digits, which show accurate or estimated digits. When we do calculations our answers cannot be more accurate than the measurements that they are based on. We must be careful to follow the following rules whenever we perform calculations in Chemistry class.

Multiplying and Dividing

RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.

Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm³

We look to the original problem and check the number of significant digits in each of the original measurements:

22.37 shows 4 significant digits.

3.10 shows 3 significant digits.

85.75 shows 4 significant digits.

Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.

5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm³.

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Adding and Subtracting

RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g

We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g

Now, be sure to check out the worksheets and the online quizzes!