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Significant Figures

The number of digits in the measured value (about the correctness of which we are sure) plus one more digit are called significant figures.
Following rules are observed in counting the number of significant figures in a given measured quantity:
  1. All non-zero digits are significant.

42.3 has three significant figures.


243.4 has four significant figures.


24.123 has five significant figures.

  1. A zero becomes significant figure if it appears between two non-zero digits.

5.03 has three significant figures.


5.604 has four significant figures.


4.004 has four significant figures.

  1. Leading zeros or zeros placed to the left of the number are never significant.

0.543 has three significant figures.


0.045 has two significant figures.


0.006 has one significant figure.

  1. Trailing zeros or zeros placed to the right of the number are significant.

4.330 has four significant figures.


433.00 has five significant figures.


343.000 has six significant figures.


  1. In exponential notation, the numerical portion gives the number of significant figures.

1.32 × 10–2 has three significant figures.


1.32 × 104 has three significant figures.


Rules for arithmetic operations with significant figures

Rule I

In addition or subtraction, the final result should retain as many decimal places are there are in the number with the least decimal places.


Rule II

In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.


Rounding off uncertain digits

Rule I

The preceding digit is raised by 1 if the insignificant digit to be removed is more than 5 and is left unchanged if the later is less than 5.


Rule II

When the insignificant digit to be removed is 5 and the uncertain digit is even, 5 is simply dropped, and if it is odd, then the preceding digit is raised by 1.


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