Significant Figures: Precision in Measurements - Online Tutor, Practice Problems & Exam Prep

Understanding significant figures is crucial for precision in scientific measurements. The number of significant figures in a value indicates its precision; more significant figures mean greater detail and accuracy. For instance, a measurement of 25.0 mL is more precise than 25 mL due to the presence of a decimal point and additional digits, signifying four significant figures compared to only two. When recording measurements, all known digits should be included, along with one estimated digit, to maintain the proper number of significant figures. This practice ensures that the inherent uncertainty in any measurement is accounted for, providing a more accurate representation of the value.

Significant Figures Precision Concept

So we know that significant figures will play a role in the way we analyze data, analyze questions. We also know what's going to have an impact on the answers that we have at the end. Now there is levels of precision that are involved when it comes to significant figures. We're going to say here the more significant figures in a measurement than the more precise it is.

So for example, a reading of 25.00 mL is more precise than just 25. That's because 25.00 mL has a decimal point. We move from left to right. Our first non-zero number here is 2 and count all the way to the end. This has four sig figs. 25, on the other hand, has no decimal point, so we move from right to left and it only has two sig figs. Since 25.00 mL has more significant figures, it's more precise. It gives us more detail.

Now when it comes to recording measurements, significant figures have to be taken into account. So we're going to say when taking a measurement, you must include all of the known numbers plus an additional decimal place. Now, we use what I call the eyeball test. It's based on an estimate or best guess from looking. So even when looking at a measuring tape or looking at a beaker, significant figures have to be taken into account.

We can't just look at the measurements or the hash marks on these tools and say that is my value because there's some level of uncertainty there. So you have to add an additional decimal place to ensure you have the correct number of significant figures. Now that we've talked about this idea of precision and measurements, click on the next video and let's put it to practice with an example question.

Significant Figures Precision Example

All right everyone, so here it says in this example question, determine the number of significant figures involved in measuring the length of the square. So in measuring the length of the square we have this measurement. We see that this here is the 3.0cm hash mark and this is 3.1 and this is 3.2.

So we see 3.2cm. Remember, with the right number significant figures, we have to add an additional decimal place. That would mean that the best answer would be 3.20cm, making options C our best choice.

Read the length of the pencil to the correct number of significant figures.

• A. 8.0 cm
• B. 8.000 cm
• C. 9 cm
• D. 9.0 cm
• E. 9.00 cm

What is the correct reading for the liquid in the burette provided below?

• A. 7 mL
• B. 7.0 mL
• C. 7.20 mL
• D. 7.00 mL
• E. 6.80 mL

Here’s what students ask on this topic:

List two situations in which measurements have an unlimited number of significant figures?

In the realm of measurements, there are certain situations where the number of significant figures is considered unlimited. These situations typically involve defined quantities or objects with inherently constant values. Here are two examples:

1. Counted Quantities: When you count discrete objects, the number of significant figures is unlimited because you're dealing with exact numbers. For instance, if you count 23 chairs in a classroom, the number 23 is exact and does not have any uncertainty associated with it, unlike a measurement that is subject to instrumental or observational error.
2. Defined Constants: Certain physical constants have an unlimited number of significant figures because they are defined values. An example is the speed of light in a vacuum, which is defined as exactly 299,792,458 meters per second. Since this is a defined value, not a measured one, it has an infinite number of significant figures. Similarly, units of measure that are defined rather than measured, such as the meter, kilogram, or second, have unlimited significant figures when used in calculations.

How many significant figures are contained in each of the following measurements?

To determine the number of significant figures in a measurement, you need to apply the rules for identifying significant figures:

1. Non-zero digits are always significant.
2. Any zeros between non-zero digits are significant.
3. Leading zeros (zeros before non-zero digits) are not significant.
4. Trailing zeros in a number with a decimal point are significant.
5. Trailing zeros in a number without a decimal point are ambiguous and may or may not be significant, depending on whether the zeros are intended as placeholders.

Let's apply these rules to some examples:

• 123.45 has five significant figures (all the numbers are non-zero).
• 0.0456 has three significant figures (the zeros are leading and not significant, but the 4, 5, and 6 are).
• 100 has one significant figure if the zeros are placeholders, but it could have three if the zeros are measured values (this is where scientific notation is helpful to indicate precision).
• 100.0 has four significant figures (the trailing zero is significant because of the decimal point).
• 0.0020 has two significant figures (the trailing zero is significant, but the leading zeros are not).

Remember, the context of the measurement and how it's written can affect the number of significant figures, so scientific notation is often used to clarify the intended precision of the measurement.

In which of the following measurements are all the zeros considered to be non-significant figures?

In measurements, zeros are considered non-significant figures when they serve merely as placeholders and do not represent a measured value. This typically occurs in two scenarios:

1. Leading zeros: These are zeros that precede all non-zero digits. They are not significant because they are only there to position the decimal point. For example, in the number $0.00456$, the first two zeros are non-significant.
2. Trailing zeros in a number without a decimal point: These are zeros at the end of a number that do not follow a decimal point. They are not significant because, without the decimal point, it is unclear if the zeros are measured or simply placeholders. For example, in the number $1500$, it is ambiguous whether the last two zeros are measured values or not, so they are considered non-significant.

Always remember that the context of the measurement and the way it is written can affect whether zeros are significant or not.