Significant Figures

Significant figures are used to state the number that is in the form of digits. These digits carry a representation of the number and are also used often instead of the figures. We can identify the significant digits of numbers by counting all the values starting from the non-zero digit situated on the left. For instance, the 12.45 number contains four significant digits.

What are significant figures?

Significant figures in a number can calculate the quantity within the expression that any scientist or engineer can measure.

Rules for significant figures:

There are three important rules for  significant figures:

1. In any case, non-zero numbers are significant: It is the obvious rule. If we measure anything with a device like a thermometer or a ruler, it gives only a number. For instance, the number 46.28, contains the four significant digits and in 5.85, there are 3 significant figures. The main problem arises when there are digits like 49.02 or 0.00750 in which zeros are present.
2. Zeros are present in the middle of any 2 significant numbers also termed as the significant number: This is the second rule that is comprehensible from the title. While the second rule perceives that any zeros present between the two significant numbers is also significant. For example,  5002 , there are 4 significant figures.
3. Zero that leads to significant numbers is used mostly in the subject of chemistry. The number of the zeros trails in the front of the different numbers that is not termed as the significant digit and non-significant. For instance, In 0.0052, total no. of significant digits is 2 because zeroes are visible and present as other non-zero nos.

Other rules

The significant figure rules include: 

Rules for the significant figures: 

• Zeros to the right of the last non-zero digit (trailing zeros) in a number with the decimal point are significant. Placing decimals is uncommon, however in this case, “450.” indicates that the zero after four and five is to be considered a significant digit. As a result, there are three significant numbers present here.
• A trailing zero in a whole number that isn’t followed by a decimal is also not termed a significant digit.
• There are an infinite number of significant digits in exact numbers. It may appear perplexing, but this rule only applies to specific numbers that appear as definitions.

In short summary of rules

• To find the number of significant figures in a given number use the below three rules: 

1. The non-zero digits are always considered significant numbers.
2. The zero between any two significant digits is considered significant.
3. A trailing zero or final zeros in the decimal portion are significant.

Eg, .544 or .456000 these zeros are significant.

.008 or .000788 these zeros are not significant

• For addition and subtraction, use the following rules: 

1. Count the no. of significant figures in a decimal portion only of each number.
2. Add or subtract as usual.
3. The final answer can not have more significant figures than the smallest number of significant figures.

Calculate significant figures with examples:

Q.1: Identify the number of significant digits/figures in the following given numbers.

0.00900 – 3 significant figures

5409 – 4 significant figures

5.00 – 3 significant figures

80.08 – 4 significant figures

Let’s take a closer look at how the concept of significant figures is used in real-world situations.

Precision

Precision refers to how near two or more quantities are to each other. When repeated, the level of measurement yields the same result.

Accuracy

It is the measuring level that gives accurate and consistent results (this means there are no systematic or random errors). The observed outcomes are consistent with the true outcomes.

The following are some of the factors that can lead to measurement uncertainty:

• If the device which is being used for measuring has limitations.
• The irregularity of the object is being measured.
• The ability and expertise of the individual tasked with measuring.
• A large number of factors can obstruct measurement since they are highly influenced and dependent on the context.

Common misconceptions about significant numbers: 

• Presuming the starting zeros of number is significant:

If we take the example of the number 0.00456, the first zeroes of these numbers are non-significant. These do not tell us the size of the number while assuming the leading zeroes. 

• Presuming all zeros in numbers are not significant:

A common error we make in determining the significant number is to assume that all zeros in a number like 8008 are not significant. When we replace the first digit number, all digits after the digit are significant.

• Not considering the zeroes to make the correct size of number

It is a common mistake when we round up the number like 378 and consider the significant figures as 38 and not 380. It is crucial to fill in the zeroes if accuracy is more than 10. 

The factors that can affect the uncertainty in measuring the number: 

– The irregularity of the object is being measured.

– The error is posted by the device when it’s being measured.

– Different other factors can come in a way while measurement as per the subject of the situation.

Conclusion 

This article explains about significant figures. Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. There are some rules explained to find significant figures, like the non-zero digits are always considered significant numbers, the zero between any two significant digits is considered significant, a trailing zero or final zeros in the decimal portion are significant, etc.