Determining Significant Figures

Understanding significant figures is crucial for students in science to ensure precision in their measurements. We discuss the importance of significant figures, their five core rules, common pitfalls in various scientific contexts, and practical strategies to help teens improve their grasp of this essential skill.

• Importance of significant figures in science 
• Five key rules for identifying significant figures 
• Common pitfalls encountered in measurements 
• Strategies for mastering significant figures 
• Resources and tools for additional support

YouTube Playlist: Significant Figures

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Transcript

Speaker 1: 0:00

If your teen is struggling with significant figures, don't worry, they're not alone. This concept can be confusing at first, but it is an essential math skill for science, especially for chemistry and physics. In today's episode, I'm breaking down significant figures into five simple rules, highlighting some key pitfalls to avoid, as well as providing some tips that you can use to support your teen in navigating significant figures. Let's dive in. 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. Before we jump into the rules, let's talk about why significant figures matter. In science, precision is key, so when we're measuring something, whether it's the mass of a chemical sample or the distance a car travels we can only be as precise as our measuring tool allows. Significant figures help scientists and engineers communicate how precise their measurements are. For example, saying something weighs 12 grams isn't the same as saying it weighs 12.0 grams, so that extra zero tells us that we measured with more precision. Now that we understand why significant figures are important, let's break down five easy to follow rules that will help your team in determining significant figures. Rule number one non-zero numbers are always significant. This is the easiest one. Any number that is not a zero one through nine is always significant. For example, the number 247 has three significant figures. We count all of them. Rule number two zeros between non-zero numbers are significant. So we call that the sandwich rule. If a zero is sandwiched between two non-zero numbers, then it counts. For example, 205,. We have a zero, but it's between a two and a five, which means we have three significant figures 1005,. That's 1,005. Even though we have two zeros, all four numbers are significant because those two zeros are sandwiched in between non-zero digits. Now this brings me to rule number three Trailing zeros are only significant if they are followed by a zero. Let's break this down. So if a number has a decimal at the end of the zero, then we do count it. If it do not, then we don't. Let's look at some examples 1400. Let's look at some examples 1,400. We only have two significant figures, which is the one and a four. The two zeros behind that are important but they are not significant. We cannot be absolutely sure that those zeros are not just placeholders for the measurement, telling us that we have 1400 instead of 14. But if we put a decimal behind that, like a little floating decimal, that doesn't make sense. But in science it makes total sense because 1400 decimal is telling people or telling other scientists that we have an exact measurement to 1400. So it's all about the precision, all about communicating our exact measurements and what we can take to the bank and what we know are just estimates. Another example can be that 205.

Speaker 1: 4:00

Let's say we have 2050. Let's say we have 2, 0, 5, 0. There we have only three significant figures because the last zero is trailing, there is no decimal. By putting a decimal behind that last zero, then we make it significant.

Speaker 1: 4:17

Now let's talk about leading zeros, which is rule number four. Leading zeros are those zeros that come before non-zero digits, for example 0.0037. In this case, those leading zeros serve the same purpose as trailing zeros they are placeholders. They are important because they tell us the degree of the number, but they are not significant. Another example can be 0.0000450. In this case we have three significant figures, even though we have a lot of leading zeros. We have four, five, followed by a zero. In that case, that last zero is significant because it comes behind a decimal and behind non-zero digits. Is your brain swimming yet? No worries, I got you In my show notes. I've linked a YouTube tutorial because sometimes seeing it is a lot easier than listening to it. So just go to my show notes, check out the video, which includes practice to help apply these rules.

Speaker 1: 5:32

Now let's talk about the fifth rule, which says exact numbers have unlimited significant figures In addition to the zeros. This one trips students up the most and this is where some numbers are considered exact and do not follow any significant figure rules at all. These are your counted values, particularly in science. These are going to be your conversion factors. For example, the conversion factor of 12 eggs equal a dozen. These are considered unlimited or infinite values because they are used to count Dimensional analysis. 1,000 milliliters equals one liter. That is also considered an infinite number and would not be considered when you're determining the number of significant figures in your final answer.

Speaker 1: 6:19

Now let's talk about some of those common pitfalls that I noticed with students in chemistry and physics. For chemistry, it can get confusing when solving stoichiometry problems, specifically when using molar mass and mole ratio. Now, calculating molar mass, you do follow the rules of significant figures. For example, calculating the molar mass of water, you have 18.02 grams per mole. That will be four significant figures. If your periodic table gave you more values, then your significant figures may be more. Your final answer must reflect the correct number of significant figures based on the measured mass from the periodic table that you're using.

Speaker 1: 7:05

Now this is not the same for mole ratio. Mole ratios come from balanced chemical equations and they have unlimited significant figures, so they follow rule number five. In other words, mole ratios are based on exact numbers, not measurements. So, for example, the chemical equation for water, where we have two hydrogen plus oxygen, yields two molecules of water. Water is a two to one ratio with oxygen. If I'm using that ratio in a stoichiometry problem, then it does not count toward my significant figures. It does not limit my final answer to one significant figure. And this works the same for dimensional analysis. For example, if I have to convert milliliters to liters or kilograms to grams, those are considered exact numbers and they do not count to limit my significant figures.

Speaker 1: 8:01

Now let's talk about a few ways to help your team master significant figures. Number one provide them with a reference guide. In class I will either print out a reference guide to give them or have them take their notes and keep that front and center to always refer back to, because they're going to have to refer to those rules and practice those rules with each calculation in order to get more comfortable with them. Second, practicing identifying exact numbers versus measured values help tremendously. Ask your team whether the number in their problem is measured or from a ratio. That alone will help them to realize how important that step is in determining the number of significant figures in their final answer. And then, third, check the work together. Make them sit down and explain to you why they use or ignore certain figures in different parts of the problem, and by them explaining it, it helps them to think about their process, their rules and fill in any gaps of misunderstanding or going back to the rules to review and refresh that they need to do.

Speaker 1: 9:14

Significant figures are going to be a part of chemistry and physics and can eat up those points on tests and exams if they're not following the rules, especially if they're taking honors or AP chemistry or physics. And by understanding how to apply these, then your team will be better prepared for those calculations that will come up and they will see higher scores. 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.