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

Significant figures are crucial in data analysis, indicating the precision of measurements. More significant figures, such as in 25.00 mL (4 sig figs), reflect greater detail than fewer figures, like 25 (2 sig figs). When recording measurements, include all known digits plus an estimated decimal place to account for uncertainty. This practice ensures accuracy in scientific calculations and enhances the reliability of results, emphasizing the importance of precision in experimental data.

Significant Figures Precision Concept

So we know that significant figures will play a role in the way we analyze data and analyze questions. We also know it's going to have an impact on the answers that we have at the end. Now there are 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, then 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 4 sig figs. 25, on the other hand, has no decimal point, so we move from right to left, and it only has 2 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 in measurements, click on the next video, and let's put it to practice with an example question.

Significant Figures Precision Example

Alright 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 3.0 centimeter hash mark, and this is 3.1 and this is 3.2, so we see 3.2 centimeters. Remember, with the right number of significant figures we have to add an additional decimal place. That would mean that the best answer would be 3.20 centimeters, making option C our best choice.

Read the length of the metal bar to the correct number of significant figures. 

• A. 15 cm
• B. 15.000 cm
• C. 20 cm
• D. 15.0 cm
• E. 15.00 cm

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

• A. 32 mL
• B. 32.30 mL
• C. 32.26 mL
• D. 32.0 mL
• E. 32.2 mL

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 measurement that carry meaning contributing to its precision. They include all known digits plus one estimated digit. Significant figures are crucial because they indicate the precision of a measurement and help ensure that calculations based on these measurements are accurate. For example, a measurement of 25.00 mL (4 sig figs) is more precise than 25 mL (2 sig figs). This precision is essential in scientific experiments to ensure reliable and reproducible results, minimizing errors and uncertainties in data analysis.

How do you determine the number of significant figures in a given measurement?

To determine the number of significant figures in a measurement, follow these rules: 1) All non-zero digits are significant. 2) Any zeros between significant digits are also significant. 3) Leading zeros (zeros before the first non-zero digit) are not significant. 4) Trailing zeros in a decimal number are significant. For example, in 25.00 mL, all four digits are significant, giving it 4 sig figs. In contrast, 0.025 has only two significant figures (2 and 5), as the leading zeros are not counted.

Why is 25.00 mL considered more precise than 25 mL?

25.00 mL is considered more precise than 25 mL because it has more significant figures. 25.00 mL has four significant figures, indicating a higher level of detail and precision in the measurement. In contrast, 25 mL has only two significant figures. The additional digits in 25.00 mL reflect a more accurate measurement, reducing uncertainty and providing more reliable data for scientific analysis.

How do you record measurements to ensure the correct number of significant figures?

To record measurements with the correct number of significant figures, include all known digits from the measuring instrument plus one estimated digit. This estimated digit accounts for the uncertainty in the measurement. For example, if a beaker shows a measurement between 25 and 26 mL, you might record it as 25.3 mL, where 25 is known, and 0.3 is estimated. This practice ensures that the measurement reflects the precision of the instrument and provides accurate data for analysis.

What is the 'eyeball test' in the context of significant figures?

The 'eyeball test' refers to the practice of estimating the last digit in a measurement based on visual inspection. When using measuring tools like a beaker or ruler, you record all known digits and add one estimated digit to account for uncertainty. For example, if a liquid level is between 25 and 26 mL, you might estimate it as 25.3 mL. This estimated digit ensures that the measurement includes the correct number of significant figures, reflecting the precision of the measurement.