Significant Figure Rules, Other Rules, Examples and FAQs

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:

1. 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.

2. 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.

3. 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 × 10^x, ‘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. 

1. 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.

2. 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.

3. 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.