Significant Figures

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Concept

A measurement that contains more number of significant figures is more accurate than a measurement that contains less number of Significant figures.


Significant Figures or SF shows the accuracy in measurements. We can understand the precision of a measurement if we know exactly the significant figures in the measurement.
For example Radius of a bob is 3.3679 cm and that of the other is 3.36 cm. In this situation the first measurement is the most accurate as it has more number of significant values of figures.

Rules of Significant Figures

We must follow the rules as given below:

  1. All the non-zero digits are SF.
    For Example:
    3.456 has four SF.
    12.3456 has six SF.
    0.34 has two SF.
  2. Zeros between non-zero digits are significant.
    For Example:
    2306 has four SF.
    20,0894 has six SF.
  3. Zeros locating the position of decimal in numbers of magnitude less than one are not significant.
    For Example:
    0.2224 has only one SF.
    0.0000034 has two SF.
  4. Final zeros to the right of the decimal point are significant.
    For Example:
    3.0000 has five SF.
    1002.00 has six SF.
  5. Zeros that locate a decimal point in numbers greater than one are not significant.
    For Example:
    30000 has only one SF.
    120000 has two SF.

Rules of Rounding Off Data

  1. If the digit to be dropped is greater than 5, then add “1” to the last digit to be retained and drop all digits farther to the right.For example:
    3.677 is rounded off to 3.68 if we need three SF in measurement.
    3.677 is rounded off to 3.7 if we need two SF in measurement.
  2. If the digit to be dropped is less than 5, then simply drop it without adding any number to the last digit.
    For example:
    6.632 is rounded off to 6.63 if we need three SF in measurement.
    6.632 is rounded off to 6.6 if we need two SF in measurement.
  3. If the digit to be dropped is exactly 5 then:
    (A) If the digit to be retained is even, then just drop the “5”.
    For example:
    6.65 is rounded off to 6.6 if we need two SF in measurement.
    3.4665 is rounded off to 6.466 if we need four SF in measurement.
    (B) If the digit to be retained is odd, then add “1” to it.
    For example:
    6.35 is rounded off to 6.4 if we need two SF in measurement.
    3.4675 is rounded off to 6.468 if we need four SF in measurement.

Remember: Zero is an even number
3.05 is rounded off to 3.0 if we need two SF in measurement.

Addition and Subtraction

In addition and subtraction, we consider the SF on the right side of decimal point. This means that only as many digits are to be retained to the right side of a decimal point as the number with fewest digits to the right of the decimal point.
For example:
4.345 + 23.5 =27.845 (actual answer by using calculator)
Answer after rounding off: 27.8

Multiplication and Division

In multiplication and division, the number obtained after calculation of two or more numbers must have no more significant figure than that number used in multiplication or division.
For example:
4.3458 x 2.7 =11.73366(actual answer by using calculator)
Answer after rounding off: 12(because 2.7 has only two significant figures)

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