Significant Figures - Online Tutor, Practice Problems & Exam Prep

Significant figures reflect the precision of measurements, with more figures indicating greater accuracy. To determine significant figures, follow two rules: for numbers with a decimal point, count from left to right starting at the first non-zero digit; for numbers without a decimal, count from right to left. This method simplifies understanding significant figures, which are crucial in calculations involving uncertainty and precision in scientific contexts.

Significant Figures

So here we’re going to say that significant figures indicate the level of precision involved with measurements and recordings. And when we get to ideas such as uncertainty, we’ll see significant figures playing a bigger role. Now, we’re going to say a number with more significant figures is more precise. Now, we’re going to say determining the number of significant figures for any given value can be easy depending on how you do it. There's a lot of rules associated with significant figures, but to make it simpler for ourselves, we’ll break it down into 2 simple ideas, and it has to do with the presence of a decimal point or not.

So if we take a look here, we’re going to say for significant figures, our first rule is this: if your number has a decimal point, you’re going to move from left to right. So we move from left to right. You’re going to start counting once you get to your first non-zero number and keep counting until the end. So our first non-zero number as we're moving from left to right is this 2. So that's where we start counting and we count all the way until the end.

So one, 2, 3. This would have 3 significant figures. Now, if your number doesn’t have a decimal point, they’re going to move from right to left. We’re going to start counting again once we get to our first non-zero number and keep counting into the end. So our first number here is 5, so keep counting all the way into the end.

So 1, 2, 3, 4. This would have 4 significant figures. And to keep significant figures easy for us to understand, we’re going to go by these two simple rules. Now there’ll be other things that pop up which we’ll talk about in the following example, but for right now, just realize that we have these two basic rules to help us with significant figures. Now that we’ve done that, let’s move on to our example.

Significant Figures

So here we're going to take a look at this example. Here it says, how many significant figures (sig figs) does each number contain? Alright. So for the first one, we're starting out with 0.00010 meters. Because it possesses a decimal point, we're going to move from left to right, and we're going to start counting once we get to our first non-zero number.

So here's our first non-zero number. Once you start counting, you count all the way until the end. So this would be 1, 2, 3, 4 significant figures for this particular value. For the next one, we have 10,000 and 30 seconds. It has no decimal point that we can see, so we're going to move from right to left.

Again, start counting once you get to your first non-zero number, which in this case would be the 3, and count all the way to the end, so 1, 2, 3, 4. So this would also have 4 significant figures. Next, we have 2.00×103 liters. We don't worry about the base and our exponent, all we care about is the coefficient because this is written in scientific notation. Because it has a decimal, we're going to go from left to right.

Our first non-zero number is this 2, and we count all the way to the end. So, 1, 2, 3 significant figures. Now finally, we have 14 people. Now this is what we call an exact number because you're not going to have 14.1 or 14.30 people.

You're going to have a whole number of people, an exact number of people. When we're dealing with exact numbers, there is actually an infinite number of significant figures. Now the chances of you seeing this all depend on your professor, but just remember when it comes to significant figures, we have 2 easy rules that we will remember in terms of decimal point or no decimal point. But when we're dealing with an exact number, there's an infinite number of significant figures because 14 people could be written as 14 people or 14.0 people or 14.0000 people. All of them are saying the same thing, and because of that, there's an infinite number of significant figures. So just remember, when we're dealing with an exact number, there's an infinite number of significant figures involved.

Significant Figures

So when it comes to significant figures, if we're doing multiplication and division, it's the measurement with the least significant figures that determines the final answer. And if we're doing addition or subtraction, then the measurement with the least number of decimal places will determine the final answer. In this example, here we need to figure out what our final answer will be with the correct number of significant figures or it's a combination of all of these different types of operations. If we take a look here, realize that we have in parentheses (0.999 + 0.01). Since they're adding, it has to be the least number of decimal places.

Here, this one has 3 decimal places and this one here only has 2. So our answer at the end has to have 2 decimal places. When we add those together, it gives me 2.009 but again we want only 2 decimal places so we'll have to round up. So that'll give me 2.01 times this one here has one decimal place, this one here has 3 decimal places. So when we subtract them, we need our answer at the end to have only 1 decimal place.

When we subtract them, what we get initially is 14.285. We want only 1 decimal place, so it rounds up to 14.3 divided by all right. So now, we're going to have here, this number here has 2 significant figures and this one here has 2 significant figures. So when we multiply them, we need a number with 2 significant figures. Plus, this one has 1 significant figure and this one has 1 significant figure.

So we have to add those two numbers together. And by adding them together, we'll get our new value, which will come out initially as 30.8 when we add those two numbers together. Or actually, 40.8. So then we have 40.8 here. Alright.

Now we're adding these 2 together. This one here has 1 decimal place. This one here has 2. So when we add those together, what we're going to get is 40.96. But again, we only want 1 decimal place because they're adding together.

So we're going to round up and it's going to give me 41.0 on the bottom. Now, if we check out each of these values, each of them has a decimal place, right? So if we follow the rules that we learned up above, we have 3 significant figures for each of them. So that means our answer at the end has to have 3 significant figures as well. So when we punch that in, we're going to get 0.701049.

But we want 3 significant figures, so it's going to come out to 0.701 as my final answer. So just remember, this is a quick refresher in terms of significant figures. Analytical chemistry is all about precision and accuracy, so we cannot forget some of these fundamental steps when doing any and all calculations that we will definitely be seeing as we proceed further and further into analytical chemistry.

Significant Figures

Hey everyone, so here it says to read the water level with the correct number of significant figures. If we take a look at this image, we'd see that the water is touching this line here and if we were to read this line, it comes out to be 7.0 milliliters. Remember, we have these little hash marks; that's because this would be 6.0, 6.2, 6.4, 6.6, 6.8, and then 7.0. And remember, that's what we see, but to get the right number of significant figures correct, you have to add an additional decimal place.

So the correct way of looking at it will be 7.00 milliliters. This would mean that option D is our correct answer.

Read the ruler measurement to the correct number of significant figures.

• A. 1.2
• B. 1.170
• C. 1.17
• D. 1.20
• E. 1.10

Read the ruler measurement to the correct number of significant figures.

 

• A. 0.7
• B. 0.6
• C. 0.70
• D. 0.68
• E. 0.60

Here’s what students ask on this topic:

What are significant figures and why are they important in scientific measurements?

Significant figures are the digits in a number that carry meaningful information about its precision. They are crucial in scientific measurements because they indicate the level of accuracy and reliability of the data. More significant figures mean higher precision. This is important when performing calculations, as it helps to ensure that the results are as accurate as the measurements allow. In scientific contexts, using the correct number of significant figures helps to communicate the uncertainty and precision of the measurements clearly.

How do you determine the number of significant figures in a number with a decimal point?

To determine the number of significant figures in a number with a decimal point, follow these steps: Start counting from the leftmost digit, moving right, and begin counting at the first non-zero digit. Continue counting all digits, including zeros, until the end of the number. For example, in the number 0.00452, the first non-zero digit is 4, so you count 4, 5, and 2, giving you three significant figures.

How do you determine the number of significant figures in a number without a decimal point?

To determine the number of significant figures in a number without a decimal point, start counting from the rightmost digit, moving left, and begin counting at the first non-zero digit. Continue counting all digits, including zeros, until the end of the number. For example, in the number 4500, the first non-zero digit from the right is 5, so you count 5 and 4, giving you two significant figures.

What are the basic rules for counting significant figures?

The basic rules for counting significant figures are: 1) For numbers with a decimal point, count from left to right starting at the first non-zero digit and include all digits until the end. 2) For numbers without a decimal point, count from right to left starting at the first non-zero digit and include all digits until the end. These rules help simplify the process of determining significant figures, which is essential for maintaining precision in scientific measurements.

How do significant figures relate to uncertainty in measurements?

Significant figures are directly related to the uncertainty in measurements. They indicate the precision of a measurement by showing which digits are known with certainty and which are estimated. The more significant figures a measurement has, the lower the uncertainty and the higher the precision. This is crucial in scientific calculations, as it ensures that the reported results accurately reflect the limitations of the measuring instruments and methods used.