Significant Figures - Definition, Rules, FAQs

Define significant figures

Significant number is also known by some other names like significant digits, precision or resolution. Whereas significant meaning in English is important or noticeable.

What are significant figures?

The number that is provided in the form of digits is established using significant figures. These digits represent numbers in a meaningful way. Instead of figures, the term significant digits is frequently used. By counting all the values starting with the first non-zero digit on the left are considered as significant numbers and from this we may determine the number of significant digits.

Also read -

• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 12 Chemistry
• NCERT Solutions for All Subjects

Definition of significant figures

Significant numbers or figures can be defined as the particular number or the digits which are able to express the meaning of the number based on its accuracy. The number 6.658, for example, includes four significant digits. These significant figures give the numbers more clarity. Significant digits is another name for them.

Significant figures examples can be considered as 13.57 in this it will include four significant digits and in case of 0.00751 then it has 3 significant figures. These all calculation of significant figure is generally based upon some rules which can be defined as follows:

Significant figures rules

There are some rules on the basis of which we can count the significant digits these rule can be explained in the manner described below:

1. All non-zero numbers are of significant nature. This can be explained by taking an example of 123456789 that contains exactly 9 significant digits.

2. Every zero which occurs between any two non-zero digits is also considered a significant number; this can be explained by taking the example of 107.0093 in which seven significant numbers are present.

In both cases counting of figures can be easily done by just counting the digits present like in the first example 123456789 digits present are nine which corresponds to 9 significant figures and in the case of 107.0093 seven digits are present which corresponds to seven significant figures.

3. Rule number three states that every zero which is present on the right hand side of a decimal point and also left to the non-zero digit is said to be non-significant in nature. This can be explained by taking the example of 0.00583 this represents only three significant figures are there as zeroes are present on left hand side which are considered as non-significant digits whereas 583 which are non-zero digits are said to be of significant nature thus 0.00583 contains only 3 significant figures.

4. This rule states zeroes which are present on the right hand side of a decimal point are said to be significant whereas a non-zero digit is not able to follow this rule. Example where this rule can be applied is 20.00 which contains four significant figures whereas if zeroes are present at the left side like 0.002 then it contains only one significant figure.

5. Rule number five states that zeroes which are on the right hand side towards zero to last digit number of decimal points are considered as significant digits whereas those which are present at left side are considered as non-significant. For example 0.0087900 in this number 5 significant digits are present whereas the zeroes in the left hand side before non-zero digit are considered as non-significant figures.

6. The last rule for finding out significant numbers considers that all the zeros which are present on the right hand side of the last non-zero digit are said to be significant if they will be found from the measurement value. For example 1234 m is considered to have 4 significant figures.

Hence these are rules by which we can easily calculate the number of significant figures present in any number whereas figures mean the presence of a number of digits in any value. It is also to be said that a natural number can contain an infinite number of significant figures like if we talk about a bag which contains 5 balls then it can also be written as 5.000000……. balls in a bag this specify that any natural number can contain an infinite number of significant figures.

Rounding off of significant figures:

By leaving one or more digits from the right, a number is rounded off to the required number of significant digits. The last digit kept should remain constant when the initial digit in the left is less than 5. The last digit is rounded up when the first digit is greater than 5. The number kept is rounded up or down to get an even number when the digit left is exactly 5. When there are multiple digits remaining, rounding off should be done as a whole rather than one digit at a time.

Rounding off any digits has rules too. These rules can be explained as the following manner:

1. At first we must determine to which digit the rounding off should be applied. If the number after the rounding off digit is less than 5 then all the numbers on the right side must be eliminated. This can be explained by taking the example of 1.24003 then rounding off will be 1.24.

2. However, if the digit next to the rounding off digit is more than 5, we must add 1 to the rounding off digit and ignore the remaining numbers on the right side. This rule is also considered as (n+1) rule. This can be explained by taking the example of 1.2478 to three figures then it is written as 1.25.

One of the main questions is often asked: why are significant figures important? This can be explained on the basis of the importance of significant figures that enable us to keep track of measurement quality. Significant figures basically show how much to round while also ensuring that the result is not more precise than our beginning number. In short we can say that it gives us a more accurate result.

Significant numbers are also an important term in maths where a significant digit can be defined as the number of digits in a value or we can say which is used frequently in a measurement of any value which contributes the most exact or we can say most precise value is known as significant figures. We start to count significant figures from the very first non-zero digit present.

Also, students can refer,

• NCERT solutions for Class 11 Chemistry Chapter 1 Some basic concepts of Chemistry
• NCERT Exemplar Class 11 Chemistry Solutions Chapter 1 Some basic concepts of Chemistry
• NCERT notes Class 11 Chemistry Chapter 1 Some basic concepts of Chemistry

Also check-

• NCERT Exemplar Class 11th Chemistry Solutions
• NCERT Exemplar Class 12th Chemistry Solutions
• NCERT Exemplar Solutions for All Subjects

NCERT Chemistry Notes:

• NCERT Notes Class 11th Chemistry
• NCERT Notes Class 12th Chemistry
• NCERT Notes For All Subjects