What Are Significant Figures?
Significant figures are usually referred to as any number of significant digits 0-9 which are wholly inclusive. A number that belongs to significant figures within an expression points to the confidence or conviction through which any engineer or any scientist asserts a quantity. In this article, we will learn about all the important concepts related to significant figures such as significant figure rules and examples. Apart from this, some measurement parameters related to significant figures are also discussed. Let’s read this article.
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Significant Figure Rules
There are various significant figure rules but out of those, the three most important rules are as follows:
Non-zero numbers are, in any case, significant:
This is one of the rules which are a bit obvious. When you try to measure something with a device such as a ruler or a thermometer, etc. and in turn, it gives you a number, then what you have done is known as a measurement decision. This process of measuring will provide significance to only that specific digit (or numeral) as of the overall number you obtain. For example, in a number such as 46.28, there are a total of four significant figures, and in 5.85, there are three. The main issue arrives when there are digits such as 0.00750 or 49.02.
Zeroes that are present between any two significant numbers are also significant:
This is another rule which is quite understandable from its title. According to the significant digit rule one, zeroes are insignificant. But the second rule states that any zero that is present between two significant numbers also turns into a significant number. For significant figure examples, in the digits 0052, there are only two significant digits. But in the digits 0502, there are a total of three significant digits because the zero between five and two are also considered significant numbers.
Zero, which leads are not significant numbers:
Used mostly as significant numbers chemistry, we do feel sorry for these leaders who are used only as a kind of placeholder for other numbers. Any number of zeroes that trail in front of different numbers are not considered a significant digit of any sort and are non-significant. For example, if the digit is 0.0052, the total number of significant digits is two because all the zeroes present and visible are leading the other non-zero numbers, which makes it non-significant for the zeroes standing in front.
A Few Other Rules
A few other significant figure chemistry rules include the following:
Trailing zeroes, which are on the right side of the decimal point, are considered to be significant.
A trailing zero amongst a whole number, with the decimal showing, is considered a significant figure. Placing decimals is not usually done, but for example, "450." incites that the following zero after four and five is to be considered as a significant digit. Thus, there are a total of three considerable numbers present here.
A trailing zero amongst a whole number, without a decimal visible, is to be considered as not a significant digit. For example, writing just "450" incites that the following zero after four and five is not to be regarded as a significant digit and thus totals the number of significant digits at two.
Exact numbers are gifted with infinite numbers of significant digits. It sounds confusing, but this particular rule only applies to specific numbers that present as definitions. For example, 3 meters can be equal to 3.000 meters or 3.000000000 meters or with more and more zeroes.
For the numbers present in scientific notation, for example, N × 10x, ‘N’ shall be considered significant figures, and “10” and “x” shall not be considered significant figures. An example of such a situation would be in “7.05 × 104,” there are only three significant figures which belong to “7.05” and those from “104” are non-significant.
Significant Figure Examples
Consider the examples of significant figures given below:
5409 - 4 the number of significant figures
80.08 - 4 the number of significant figures
5.00 - 3 the number of significant figures
0.00900 - 3 number of significant figures
Some Measurement Parameters Related to Significant Figures
Let's dive a bit more into this and know more about what are significant digits.
Accuracy:
The accuracy of measurement represents the closeness between the measurement and the absolute value of the measurement. For example, take an A4 size paper that is commonly used in computer printers and copy machines. Assuming the package of the paper states that the length of the paper was 10-inch long. You take out a ruler and measure it three times. The following results - 10.1 inches, 10.2 inches, and 9.9 inches are obtained in the three measurements. Now if you calculate the average measurement is 10.06 then the given measurement is said to be highly accurate.
Precision:
The precision in the measurement system refers to the closeness between the various repeated measurements taken under similar conditions. Let’s bring back the A4 sheet example. The precision of a measurement can be observed between the different measured values. One of the ways to derive accuracy is to determine the varied difference between the lowest and highest values.
In the paper case, the lowest is 9.9 inches and the highest standing at 10.2 inches, respectively. So, the deviated measured value amidst the lowest and highest is 0.3 inches. This result is relatively precise because it merely varies much in the case of value. If the measurement value would have been something like 9.9 inches, 10.1 inches, and 10.9 inches, then there wouldn't be any talk of precision because it wouldn't be precise at all.
Uncertainty:
It is a parameter that is used to express the amount of uncertainty about the true value. Uncertainty is usually denoted by less significant figures than the measured quantity itself as there is no meaning of describing uncertainty more precisely than the measured value. Consider the following examples to understand this better:
235.0 +/- 0.5m/s tells us that we are not sure about the last digit of the quantity ‘235.0m/s’ by the uncertainty of +/-0.5m/s.
Writing 21.1 +/- 0.25467L is inappropriate. It should be written as 21.1 +/- 0.3L.
Writing 448.45 +/-10cm is incorrect. 450 +/- 10cm is correct.
Factors that can contribute to uncertainty taking place in measurements are as follows:
Limitations posed by the devised being used for measurement
The object’s irregularity is being measured
The skills and talent the person has to measure. Different factors can come in the way of measurement because these are very much influenced and subject to the situation
Conclusion
As we come to the end, let us recollect that we have discussed what are significant figures and their importance in engineering and measurement. Also, we have defined a few keywords such as ‘Accuracy’, ‘Precision’ and ‘Uncertainty’ on the basis of our understanding of significant and non-significant figures.
FAQs on Significant Figure Rules, Other Rules, Examples and FAQs
1. What are the main rules for determining significant figures in a number?
The primary rules for identifying significant figures, which are crucial for expressing the precision of measurements in chemistry, are as follows:
- Non-zero digits: All non-zero digits (1 through 9) are always significant. For example, the number 285 has three significant figures.
- Captive zeros: Zeros that are placed between two non-zero digits are always significant. For instance, 40.07 has four significant figures.
- Leading zeros: Zeros that come before all non-zero digits are never significant. They act only as placeholders. For example, 0.0052 has only two significant figures (5 and 2).
- Trailing zeros: Their significance depends on the presence of a decimal point. Zeros at the end of a number are significant only if a decimal point is present. For example, 5.00 has three significant figures, but 500 has only one. The number 500. (with a decimal) has three significant figures.
2. How do you apply significant figure rules in calculations involving addition/subtraction and multiplication/division?
The rules for significant figures in calculations differ based on the mathematical operation:
- For Multiplication and Division: The final result should have the same number of significant figures as the measurement with the least number of significant figures. For example, if you multiply 4.56 (3 significant figures) by 1.4 (2 significant figures), the result 6.384 should be rounded to 6.4 (2 significant figures).
- For Addition and Subtraction: The final answer should have the same number of decimal places as the measurement with the fewest decimal places. For example, when adding 12.11, 18.0, and 1.013, the number 18.0 has the fewest decimal places (one). The sum is 31.123, which should be rounded to 31.1.
3. When are zeros considered significant figures?
Zeros are considered significant in two main situations:
- When they are 'captive', meaning they are located between two non-zero digits. For example, in the number 7003, both zeros are significant, making a total of four significant figures.
- When they are 'trailing' and appear after a decimal point. These zeros indicate the level of precision. For instance, in 92.00, both zeros are significant, indicating the measurement is precise to the hundredths place, giving it four significant figures. A zero at the end of a whole number like 120 is not significant unless written as 120. or in scientific notation.
Leading zeros, such as those in 0.045, are never significant.
4. Why are significant figures important in chemistry and other sciences?
Significant figures are fundamental in sciences like chemistry because they communicate the precision of a measurement. Every measurement is limited by the instrument used. Using the correct number of significant figures ensures that a calculated result is not reported as being more precise than the measurements used to derive it. This practice prevents reporting misleading data and is crucial for the reliability and reproducibility of scientific experiments.
5. How do significant figures relate to the precision and accuracy of a measurement?
Significant figures are directly linked to the concept of precision.
- Precision refers to how close multiple measurements of the same quantity are to each other. A greater number of significant figures implies a more precise measurement. For example, measuring a length as 5.45 cm is more precise than measuring it as 5.4 cm.
- Accuracy, on the other hand, refers to how close a measurement is to the true or accepted value. While significant figures indicate precision, they do not guarantee accuracy. A precise instrument can be improperly calibrated, leading to results that are precise but not accurate.
6. What is the difference between an exact number and a measured number in the context of significant figures?
The distinction is crucial for calculations:
- Measured Numbers: These are obtained using a measuring instrument (like a ruler, balance, or graduated cylinder) and thus have a limited number of significant figures, reflecting the instrument's precision.
- Exact Numbers: These have an infinite number of significant figures. They are known with complete certainty and do not limit the number of significant figures in a calculation. Exact numbers come from two sources:
- By definition (e.g., 1 metre = 100 centimetres, 1 dozen = 12 items).
- From counting discrete objects (e.g., 8 students, 3 beakers).
7. Why are trailing zeros in a whole number like 6500 ambiguous, and how does scientific notation resolve this?
The number 6500 is ambiguous because it's unclear whether the measurement was precise to the nearest hundred (6500, two significant figures), the nearest ten (6500, three significant figures), or the nearest one (6500, four significant figures). This ambiguity is a major reason why scientists prefer scientific notation.
Scientific notation removes all doubt:
- 6.5 x 10³ clearly indicates two significant figures.
- 6.50 x 10³ clearly indicates three significant figures.
- 6.500 x 10³ clearly indicates four significant figures.
By using scientific notation, we explicitly state which digits are significant, thereby communicating the exact precision of the measurement.
