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4 PHYSICS This shows that the location of decimal point is negative exponent (or power) of 10. In order to of no consequence in determining the number get an approximate idea of the number, we may of significant figures. round off the number a to 1 (for a≤5) and to 10 The example gives the following rules : (for 5<a ≤ 10). Then the number can be • All the non-zero digits are significant. expressed approximately as 10 in which the • All the zeros between two non-zero digits exponent (or power) b of 10 is called order of magnitude of the physical quantity. When only are significant, no matter where the an estimate is required, the quantity is of the decimal point is, if at all. order of 10 . For example, the diameter of the earth (1.28×10 m) is of the order of 10 m with • If the number is less than 1, the zero(s) on the right of decimal point but to the the order of magnitude 7. The diameter of left of the first non-zero digit are not hydrogen atom (1.06 ×10 –1m) is of the order of significant. [In 0.00 2308, the underlined 10 –10m, with the order of magnitude –10. Thus, the diameter of the earth is 17 orders zeroes are not significant]. • The terminal or trailing zero(s) in a of magnitude larger than the hydrogen atom. It is often customary to write the decimal after number without a decimal point are not the first digit. Now the confusion mentioned in significant. (a) above disappears : [Thus 123 m = 12300 cm = 123000 mm has 2 4.700 m = 4.700 × 10 cm three significant figures, the trailing zero(s) = 4.700 × 10 mm = 4.700 × 10 km –3 being not significant.] However, you can also see the next observation. The power of 10 is irrelevant to the determination of significant figures. However, all • The trailing zero(s) in a number with a zeroes appearing in the base number in the decimal point are significant. scientific notation are significant. Each number [The numbers 3.500 or 0.06900 have four in this case has four significant figures. significant figures each.] Thus, in the scientific notation, no confusion arises about the trailing zero(s) in the base (2) There can be some confusion regarding the trailing zero(s). Suppose a length is reported to number a. They are always significant. be 4.700 m. It is evident that the zeroes here (4) The scientific notation is ideal for reporting are meant to convey the precision of measurement and are, therefore, significant. [If measurement. But if this is not adopted, we use these were not, it would be superfluous to write the rules adopted in the preceding example : • For a number greater than 1, without any them explicitly, the reported measurement would have been simply 4.7 m]. Now suppose decimal, the trailing zero(s) are not we change units, then significant. • For a number with a decimal, the trailing 4.700 m = 470.0 cm = 4700 mm = 0.004700 km zero(s) are significant. Since the last number has trailing zero(s) in a number with no decimal, we would conclude (5) The digit 0 conventionally put on the left of a erroneously from observation (1) above that the decimal for a number less than 1 (like 0.1250) number has two significant figures, while in is never significant. However, the zeroes at the fact, it has four significant figures and a mere end of such number are significant in a change of units cannot change the number of measurement. significant figures. (6) The multiplying or dividing factors which are (3) To remove such ambiguities in determining the number of significant neither rounded numbers nor numbers representing measured values are exact and figures, the best way is to report every have infinite number of significant digits. For measurement in scientific notation (in the power of 10). In this notation, every number is example in r =d or s = 2πr, the factor 2 is an expressed as a × 10 , where a is a number 2 exact number and it can be written as 2.0, 2.00 between 1 and 10, and b is any positive or Reprint 2026-27