Teaching High School Science

Summer Prep Series: Significant Figure for Chem and Physics

• Kesha "Doc" Williams • Episode 34

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If your teen is preparing for chemistry or physics this year, especially at the honors or AP level, significant figures are one of those early concepts that can trip them up and quietly cost points all year long.

In this episode of Teaching High School Science, I’m breaking down what significant figures (or "sig figs") really are, why they matter in science, and how to help your teen build strong habits now to avoid common mistakes later.

You’ll learn:

  • The five essential rules for identifying significant figures (with examples!)

  • When to focus on decimal places for addition and subtraction

  • Why total sig figs matter in multiplication and division

  • How to handle mixed operations and use PEMDAS without losing points

  • Simple strategies like creating a problem notebook and using verbal explanations to strengthen understanding

Whether you're supporting your teen at home or in the classroom, these tips will help them feel more confident and accurate when using sig figs—so they can focus on the science instead of getting stuck on the formatting.

📩 Be sure to check the show notes for:

  • A free Significant Figures Guide

  • A blog post with visual examples and step-by-step explanations

🎧 Tune in and help your teen start the year strong with the precision skills they’ll use all year long in both chemistry and physics.


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Let's continue the conversation and explore the wonders of science together!


Speaker 1:

If your teen is prepping for chemistry or physics this year, one concept that trips students up early and keeps showing up all year is significant figures, especially if they're taking honors level chemistry or physics, or AP chem or physics. So today I'm breaking down what they are, why they matter and how to help your teen avoid losing points with simple mistakes. Welcome to Teaching High School Science. I'm your host, doc, a former biochemist turned high school science teacher and private tutor. Whether you're homeschooling your teen through high school science or teaching online, join me as I share tips and strategies I've learned over the years for at-home and online labs and activities, breaking down complex concepts and structuring learning in a way that makes sense. Now let's dive into today's topics. I've also got a free guide and a blog post that shows each step in action. Both are linked in the show notes. Let's start with the why.

Speaker 1:

In science, we use significant figures, or sig figs, to show how precise a measurement is. They tell us which digits in a number are meaningful, based on the tool or the method used to take that measurement. This becomes important in both chemistry and physics, where calculations are based on measured values. Students need to report answers that reflect the correct level of precision and when teachers, especially on exams, expect the correct sig figs to be used. And while it may seem like a small formatting issue, it really speaks to the precision of the measurement. So where 1,000 is an important number, it only has one significant figure, because I can only guarantee that measurement to that first non-zero digit. How do I know that there's only one sig fig in 1,000 versus the four important numbers in 1,000? Because, let's face it in 1,000. Because, let's face it, one being a significant figure is very important in science, but 1,000 is a lot different from one. So how did I know that? Well, let's go through some of the rules for identifying which numbers in a value are significant. There are five rules that I want to go over. Now, before I go over these rules, I want to remind you that the blog post illustrating each of these rules is linked in a show notes. So if you benefit from more of a visual way of looking at this, go ahead and check out the blog post and it will also give you a link to the free guide that you can use with your students to help remind them of these rules, that you can use with your students to help remind them of these rules.

Speaker 1:

Now for the first rule all non-zero digits are always significant. For example, one, two, three, all the way through nine. Those are digits that are non-zero and they are significant. So if I have a number of 123, I have three significant figures. If I have a number of 1453, I have four significant figures. The second rule any zeros between non-zero digits are significant. So 105, because the zero is between a one and a 5, that's 3 significant figures. 1,005, because those two 0s are sandwiched between the 1 and the 5, that's 4 significant figures. However, trailing 0s are not significant. If I were to have 1,500, 1,500, no decimal, then that means I only have two significant figures, the one and the five, because my two zeros are not sandwiched and there is not a decimal behind those zeros.

Speaker 1:

This brings us to our next rule, which is trailing zeros are significant only if there's a decimal point. For example, 1500, one, five, zero, zero. There is no decimal point and the zeros are trailing behind the five. So that means that there are two significant figures, the one and the five, and those two zeros, even though they're important, they are not significant because whatever instrument was used to make that measurement did not include exact digits for those places. However, it's important to include those numbers because 15 is different than 1500. So I can only guarantee the measurement to the one and a five. However, if I were to put a decimal behind that last zero, that would be 1500 decimal point. Then that means I have four significant figures and I'm telling other scientists that my instrument measured one, five and two zeros. It was that precise. Now I cannot put another zero behind that decimal because it looks funny. Then I will have five significant figures. So it's important to understand that in science, when we're talking about measured values, sometimes the writing is not as conventional as what you would have in real life. 1500 decimal is extremely important because that's telling us that we have four significant figures instead of just two.

Speaker 1:

Let's talk about a fourth rule. What about leading zeros? Leading zeros are never significant. For instance, 0.0025. That has two significant figures, the two and the five. Unless those zeros become sandwiched, they are not significant. So if I have 0.0123, then I have one, two, three that are significant, which are three significant figures. If I have four 0.0123, then all of those numbers become significant. Notice that four in front of that first zero makes those two zeros in the center sandwich. So the 400123 are all significant, giving me six significant figures. And again, if this is just making your brain just want to explode and you need that visual representation of it, check out the link in my podcast notes and grab that blog post.

Speaker 1:

The fifth rule is all about counting numbers, which says that counting numbers have an infinite number of sig figs. What we are referring to here are those known values. If you missed the episode about dimensional analysis where I talk about conversion factors, these are what I mean by known values. Go back and check that out. The example I used there would be 12x equal one dozen. If we're using that in dimensional analysis and converting, we know, no matter what we have, that 12 of anything is a dozen. Whether it's 12 paperclips, 12 apples, 12 feathers, that's a dozen. So if I have to use that within my calculations, then I do not count that toward my sig figs. However, if I'm using something like molar mass, where we have to use values from the periodic table and calculate the mass per gram of a substance, then that is considered part of our significant figures because we're using a measured value. So rule five can become a bit tricky. You just have to pay attention to which are known values and which are measured values that you're using as your conversion factor. Now let's talk about when we're using measured values in calculations.

Speaker 1:

Each of the rules that we just discussed will be applied to each measurement or number that is in our calculation, because we will then use that to determine how many significant figures our final answer will have. So let's look at the rules for addition and subtraction. When you're adding or subtracting numbers, the rule is based on the decimal places, not the total number of digits. So the answer must be rounded to match the number with the fewest decimal places in the problem. And that is because if I have a measurement with four significant figures and then I have another measurement with five significant figures, well I can only be as certain of the measurement as the four significant figures. I can't make another significant figure be added to the one that only has four. So I always have to take the number within my calculation of the least number of significant figures For adding and subtracting. I have to pay attention to that decimal.

Speaker 1:

Let's look at an example. Let's say I am adding 12.11 to 0.3. Now 12.11 has four significant figures, because all of those numbers are non-zero. However, 0.3 only has one significant figure because that zero is leading. We don't count it, so we only have the three. When I add those two numbers together, the answer is 12.41. Now while 12.41. Now, while 12.41 has four significant figures. Well, my 0.3 only had one and if I'm lining those decimals up, then I'll only have one decimal place. So I'm going to round that to 12.1, which is one decimal place. So, having your team to line up the decimal points when they're adding and subtracting, and then taking a highlighter and highlighting straight down the last decimal place of the smallest answer, then that will help them to know how many decimal places they need to include in their final answer to be correct for sig figs.

Speaker 1:

Now let's talk about multiplying and dividing with significant figures. It's all about the total number. We are not worried about decimals, we are worried about the total number. So the final answer will have the same number of sig figs as the measurement with the least number. So let's say I'm multiplying 4.56 by 1.4. 4.56 has three significant figures and 1.4 has two significant figures. We're not even worried about the decimal points. The final answer for that would be 6.384. Well, my number with the least number of sig figs is 1.4, which is two significant figures. So my answer will round to 6.4. And remember the rules for rounding. You look at the number right behind the number that you want. If it's five and up, then you round up. And that is why the final answer is 6.4, which is two sig figs.

Speaker 1:

What if the problem includes both subtraction and multiplication? That's a mixed operation and that can be seen in problems where you may be calculating specific heat or other types of problems in either chemistry or physics, where you have multiple steps in the equation in order to get the final answer. So here's a strategy that I have students do. I have them pay attention to the significant figures at each step. You have to follow PEMDAS when you're solving the problems. So at each step, determine your number of significant figures, take that and then follow that into the next step.

Speaker 1:

For example, let's say I am having to calculate the difference in a temperature and then multiply that by a different factor. So let's say I have 5.12 minus 3.1 and then that answer has to be multiplied by 2.00. So the first thing I'm going to do is take care of my subtraction. 5.12 has three significant figures, two decimal places where 3.1 has two significant figures, one decimal place. Because this is a subtraction problem, I have to line up my decimal places. I will have 2.02, where that answer can only be as strong as my least number of decimal places, which is one. So that means that that final answer for that subtraction problem would round to 2.0. Now I'm going to take 2.0 and multiply that by 2.00. I have 2.0, which is two sig figs, and I have 2.00, which is two sig figs, and I have 2.00, which is three sig figs, not worried about decimal places, because this is multiplication. In this case, two times two is four. But I need to have two sig figs because my least number of sig figs is 2.0, and my answer will be 4.0, which is two sig figs.

Speaker 1:

As you can imagine, this will come with practice. So here are some ways that you can help your team practice these types of problems. If you listened to my last podcast, I talked about that problem notebook where you have examples. You have a dedicated page that has examples of counting sig figs, the rules for addition and subtracting, for multiplying and dividing, as well as for mixed problems. Talking out is a powerful tool because they hear what they're doing and I've noticed that my students in class. They will start talking to themselves because they know that it helps them to organize that information in their minds, for them to be able to logically think about it. And some tools that I have for you to help you would be that free SigFigs guide which is linked in my show notes. It provides the rules to SigFigs that will help them remember them and can serve as a year-long reference, as long as the blog that gives visual examples.

Speaker 1:

So just keep in mind that significant figure shows up early and often in both chemistry and physics. Helping them to develop these habits now will help the SMU year go smoother and avoid losing points on assignments and exams. Let me know if you have any questions, ideas or other experiences that you'd like to share. Head on over to my podcast page, which you can access by visiting my website at thesciencementorcom. Then select podcast from the menu and subscribe now to the teaching high school science podcast for your regular dose of motivation and, just in time, science ideas, and together let's make high school science a journey of exploration and achievement. Until next time, remember curiosity leads to endless possibilities.