Significant Figure Rules

What are Significant Figures?

Significant figures are usually referred to any number of significant digits, 0-9 are wholly inclusive. A number which belongs to significant figures within an expression points to the confidence or conviction through which any engineer or any scientist asserts a quantity.

Significant Figures Rules

There are various significant figure rules but out of those, the three most important rules are -

#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 place holder for other numbers. Any number of zeroes that trail in front of different numbers are not considered as 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 

Few other significant figure chemistry rules include-

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 an 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.

Numbers present in scientific notation, for example, N × 11x, are considered significant figures, and “10” and “x” are not to be considered significant figures. An example of such a situation would be, in “7.05 × 11(4),” there are only three significant figures, “7.05” and “10(4)” are non-significant figures. 

Significant Figures Examples

A few examples of significant figures are –

  • 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

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. 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 to give out the following results - 10.1 inches, 10.2 inches, and 9.9 inches. Now, if you were to calculate and find that the measurement is 11 inches or 12 inches, you would not be near 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 is referred to 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, lowest being 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 inch. This result is relatively precise because it merely varies much in 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.

Factors which can contribute to uncertainty taking place in measurement are:

  • 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 which can come in the way of measurement, because these are very much influenced and subject to the situation.

FAQ (Frequently Asked Questions)

1. When can Zeroes be Considered as Significant?

Ans: Any zeros that are present between two digits are considered significant.

2. Why are Zeros at the End of the Number not Considered Significant?

Ans: The first zero that is not present between any two significant figures, and is not present towards the right of the decimals, is not considered significant.

3. Do the Answers Need to be Written in Decimal or Scientific Notation?

Ans: The answers can be in the form of decimal or scientific notation. Scientific notations are easier to read and work with.

4. When can we Round the Result to Get a Significant Number in the Account?

Ans: You can round up the result when the first digit can be discarded or is higher than the number 5.

5. What are the Three most Crucial Significant Figure Rules?

Ans: These are the three most important rules of significant figures:

  • Non-Zero figures can always be significant.

  • Any zeros that is present between two significant digits are still significant.

  • A final or trailing zero is significant only when it’s in the decimal portion.