Significant Figures: Precision in Measurements: Videos & Practice Problems

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

Understanding significant figures is crucial for accurate data analysis and measurement interpretation. The concept of significant figures relates directly to the precision of a measurement; the more significant figures present, the more precise the measurement is. For instance, a measurement of 25.00 mL is more precise than 25 mL because the former includes a decimal point, indicating a higher level of detail. In this case, 25.00 mL has four significant figures, while 25 mL has only two.

When recording measurements, it is essential to consider significant figures carefully. The rule of thumb is to include all known digits plus one estimated digit. This practice acknowledges the inherent uncertainty in measurements. For example, when using a measuring tape or a graduated cylinder, one should not simply read the measurement from the markings; instead, an additional decimal place should be added based on a visual estimation, often referred to as the "eyeball test." This approach ensures that the recorded value reflects the appropriate level of precision.

In summary, significant figures play a vital role in scientific measurements, influencing the accuracy and reliability of data. By adhering to the principles of significant figures, one can enhance the quality of their measurements and analyses.

Significant Figures Precision Example

When determining the number of significant figures in a measurement, it is essential to understand how to accurately represent the precision of that measurement. In this example, the length of a square is measured at 3.2 centimeters, with hash marks indicating the values of 3.0, 3.1, and 3.2 centimeters. To express this measurement with the correct number of significant figures, it is important to include an additional decimal place. This practice reflects the precision of the measurement taken. Therefore, the most accurate representation of the length is 3.20 centimeters, which indicates that the measurement is precise to the hundredths place. This makes option C the best choice for the answer.

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

Answer: (E)

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

Answer: (D)

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.