## Significant Figures

#### Aligned To Common Core Standard:

**High School** - HSN-Q.A.3

What are Significant Figures? When rounding off figures, you must consider many different things or keep a lot of things running around in your mind. Particularly, when you are required to round off the digit to an appropriate number of significant figures. Are you taking this into consideration when make your calculations now? If you are not doing this when you are making calculations that involves measurements, you may be neglecting an important piece of information that is greatly affecting your level of precision. This can ultimately mean the difference between a successful experiment and a colossal waste of your time. These values are the digits that provide valuable or useful information about the accuracy of a measurement. They contribute to the value of a number and give it a meaning. There are a few basic rules that apply to determine which digits are significant. When you are evaluating a value, the following figures are considered significant: 1) All non-zero digits. 2) Any zeros between those non-zeroes. 3) Zeros that are trailing to the right of a decimal point in a decimal number. When adding or subtraction values these rules apply to maintain a high level of accuracy: 1) Count on the significant figures in the decimal portion of the numbers that are involved. Note the value that as the least number of sig. figs. 2) Add or subtract the values. 3) Your final answer can have no more than the sig figs than the starting value that had the least number of sig figs. When we apply this to multiplication and division, it follows the same rule. Our final answer has the same level of accuracy as the least accurate starting value. Note that these digits are widely used for scientific measurements. Below you find a large selection of worksheets and lessons that help students recognize and understand the proper degree of accuracy they must express their answers in.

### Printable Worksheets And Lessons

- How Many with Significant Figures? Lesson- We help students through the use of three critical rules. Rule 3 trips them up the most.
- Operations with Significant FiguresIn Mind Lesson- Just remember that your answer has to be as accurate as the least accurate value you were given.
- Guided Lesson - Four sig fig naming problems followed by a simple difference that must be placed in the proper number of sig figs.
- Guided Lesson Explanation - The previous version of this referred to numbered rules, but we found that teachers and students were confused if they had their own rule set.
- Identification Activity - All we want to know is how many sig figs you see.

#### Significant Digit Identification Worksheets

They more difficult as you move up through the sequence.

- Practice Worksheet 2 - Identify the starting values that are present for each value.
- Practice Worksheet 3 - All non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9) are always considered significant.
- Practice Worksheet 4 - Any zero (0) located between these digits are significant.

#### Significant Figures In Operations Worksheets

You should start the problem by identifying the value with the least number of sig figs. That's the number of sig figs your answer needs to be in.

- Adding and Subtracting with Significant Figures Worksheet 1 - Find the sum or difference and round your answer to the proper value based on the significant digits present.
- Adding and Subtracting Worksheet 2 - When a decimal point (.) is present, all ending or trailing zeros in the decimal portion are significant.
- Adding and Subtracting Worksheet 3 - You should always look for a decimal point first to see how to proceed.
- Multiplying and Dividing with Significant Figures Worksheet 1 - Find the product or quotient and round your answer to the proper value based on the significant digits present.
- Multiplying and Dividing Worksheet 2 - To this we look at the number of significant digits that were present in the values we were asked to perform the operation on.
- Multiplying and Dividing Worksheet 3 - Our final answer needs to be in the same number of significant digits as the least accurate (fewest significant digits) value we started with.

### Who Worries About Significant Figures Anyway and Why It Matters?

In the real-world accuracy matters. You can only be as accurate with any measure as the tools or the equipment you are using to take measures. When reporting your results of any experiment or reading, this must be stated so that a level of validity can be attributed to your work by others. When you take a value and pop it into your calculator the end value is “appropriate” in the sense of the math behind it, but there is a level of uncertainty behind that value. The level of uncertainty is ascertained by the type of device that was used to establish the numbers. An example can be found on a construction yard any where in the world right now. If three different carpenters used three different measurement tools to find the length of a piece of a decking board, they may have different readings. With a standard metric tape measure the first carpenter may get a reading of 23.9 cm. The second carpenter uses a more accurate tape measure and a reading of 23.96 cm. The last carpenter uses a laser echo device and gets a reading of 23.954147 cm. This leaves use with a bit of an accuracy problem. Which of these values exhibits that proper level accuracy? We need to remember that our end value or answer to lie where your least accurate starting value began. You will find the level of accuracy constantly criticized by economists, scientists, and statisticians. You find that sports that involve time like track and swimming events are considering this value as well. In those athletic events a standard level of precision is determined by tools used to record the time. In the end, we report values that we would have a high level of certainty in.