What are the 5 Rules for significant figures?

Significant figures are the number of digits in a value, often a metric, that add to the degree of accuracy of the value.

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What are the 5 Rules for significant figures?

 Rule 1: All non-zero digits are considered significant.

This implies that all digits 1 to 9 are significant.

For example: 489.67 has five significant digits.

345,643,267 has nine significant figures.

3.68 has three significant figures or digits.

Rule 2: Zeros between two non-zero digits are significant.

340.61has five significant digits. The zero is significant on the grounds that it comes between the 4 and the 6 which are also significant.

Rule 3: If there are zeros to the left of an understood decimal point in a whole number, however to the right of a non-zero digit, the situation becomes questionable.

There is an understood decimal point in the number 402000 after the specified six digits. There are 3 zeros that lie to the left of the decimal point that is understood, yet to the right of a non-zero number, so the condition becomes doubtful.

If it is expressed as 3.15 × 10⁵, it turns out to be clear and we can say that 3.15 × 10⁵ has 3 significant figures. It is represented as 3.15 × 10⁵, so the number of significant figures is 4.

Rule 4: All zeros which are to the right of the decimal point however to the left of the non-zero number are not significant in a decimal number that lies between 0 and 1.   

For example:

Example 5: 0.035 has two significant digits. For finding the decimal point, the zeros are placeholders.  Example 6: 0.01060 has four significant digits. Placeholders are the initial two zeros and are not significant. The third zero is significant on the ground that it falls between two other significant digits. The fourth zero is significant on the ground that it is specifically included as the last digit in a measurement.

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Rule 5: Trailing zeros could conceivably be significant in a number without a decimal point.

Example 7: There may be two, three, or four significant figures in 2100.

Example 8: There may be 2 or 3 significant figures in 350. By writing the numbers in scientific notions, this complexity can be avoided.

Other Rules

Besides this, the other rules for significant figures are:

A) Addition and Subtraction

Look at the decimal part (i.e., to the right of the decimal point) of the numbers just for addition and subtraction.

The process involves:

1) First, in the problem in the decimal section, you can count the number of significant figures for each number. (Digits to the left of the decimal position are not used to determine the number of decimal places in the final answer.)

2) After that, you should Add or subtract in the normal way.

3) In the problem round the answer to the least number of places in the decimal portion of any number.

Note: The add/subtract rules vary from the multiply/divide rules. Swapping all sets of rules is a very normal student mistake. Using only one rule for all forms of operations is another typical blunder.

B) Multiplication and Division

The accompanying rule applies to multiplication and division: the least number of significant figures in any number of problems decides the number of significant figures in the answer. This implies you should know how to identify significant figures in order to apply this rule.

Example 1: The answer to this will be 8.6. (The calculator reading is 8.55 however after rounding it becomes 8.6). Why? 2.5 has two significant figures, while 3.42 has three significant figures. Two significant figures are less precise than three, thus the answer has two significant figures.

Example 2: How many significant figures will this 3.10 x 4.520 have? Maybe you have said two. That’s so few.  For the student it is a typical mistake to look at a number such as 3.10 and assume it has two significant figures. The zero in the hundredth’s place is not perceived as significant when, indeed, it is. 3.10 has three significant figures. Thus, three is the right answer. 14.0 has three significant figures. Note that the in the tenth’s place zero is considered significant. Both trailing zeros are viewed to be significant in the decimal section.

Note:

1) The rules for determining relevant multiplication and division statistics are contradictory to the rules for addition and subtraction. Only the cumulative number of significant figures in each of the factors matters for multiplication and division; the decimal position of the last significant figure in each factor is insignificant. Only the decimal position of the last significant figure in each of the terms is important for addition and subtraction; the total number of significant figures in each word is meaningless. Nonetheless, if any non-significant digits are maintained in intermediate results which are utilised in subsequent measurements, better accuracy can always be achieved.

C) Logarithmic or natural logarithmic quantities

A natural logarithm is the power to which base e should be raised. The whole number portion of the logarithmic quantity shall decide the magnitude, similar like the power of ten in a number expressed in scientific notation, and the decimal portion will provide the numeric value.

The digits in the coefficient are significant in scientific notation. In terms of significant figure, the exponent is not considered.

Example 1: 2.100x 103 will have 4 significant figures with certainty.

Example 2: With certainty, 3.50 x 103 would have 3 significant figures.

Example 3:  11:3.54 x 105 has three significant digits.

Example 4: 1.6340 x 10-6, for example, has five significant digits.  

D) Formulas containing constants

The numbers known with full certainty are supposed to be exact. Conversion variables, constants, values that are part of the formula are said to be exact. This “exact” number are considered to have an indefinite number of significant figures and are never used as a limited factor in deciding the number of significant figures resulting from the operation.

Example 1: 1 cm = 10 millimeters. The number 10 would have an infinite number of significant figures.

Example 2: radius = diameter/2. The 2 would have an infinite number of significant figures.

Example 3: π (pi) would have an infinite number of significant figures.

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