<P> The part of the representation that contains the significant figures (as opposed to the base or the exponent) is known as the significand or mantissa . </P> <P> The basic concept of significant figures is often used in connection with rounding . Rounding to significant figures is a more general - purpose technique than rounding to n decimal places, since it handles numbers of different scales in a uniform way . For example, the population of a city might only be known to the nearest thousand and be stated as 52,000, while the population of a country might only be known to the nearest million and be stated as 52,000,000 . The former might be in error by hundreds, and the latter might be in error by hundreds of thousands, but both have two significant figures (5 and 2). This reflects the fact that the significance of the error (its likely size relative to the size of the quantity being measured) is the same in both cases . </P> <P> To round to n significant figures: </P> <Ul> <Li> Identify the significant figures before rounding . These are the n consecutive digits beginning with the first non-zero digit . </Li> <Li> If the digit immediately to the right of the last significant figure is greater than 5 or is a 5 followed by other non-zero digits, add 1 to the last significant figure . For example, 1.2459 as the result of a calculation or measurement that only allows for 3 significant figures should be written 1.25 . </Li> <Li> If the digit immediately to the right of the last significant figure is a 5 not followed by any other digits or followed only by zeros, rounding requires a tie - breaking rule . For example, to round 1.25 to 2 significant figures: <Ul> <Li> Round half up (also known as "5 / 4") rounds up to 1.3 . This is the default rounding method implied in many disciplines if not specified . </Li> <Li> Round half to even, which rounds to the nearest even number, rounds down to 1.2 in this case . The same strategy applied to 1.35 would instead round up to 1.4 . </Li> </Ul> </Li> <Li> Replace non-significant figures in front of the decimal point by zeros . </Li> <Li> Drop all the digits after the decimal point to the right of the significant figures (do not replace them with zeros). </Li> </Ul>

Rules for identifying the number of significant figures