of the used data in the calculations, or in a measurement reported to a greater precision than the measurement resolution. Of the significant figures in a number, the most significant is the digit with the highest exponent value (simply the left-most significant figure), and the least significant is the digit with the lowest exponent value (simply the right-most significant figure). For example, in the number "123", the "1" is the most significant figure as it counts hundreds (102), and "3" is the least significant figure as it counts ones (100). Significance arithmetic is a set of approximate rules for roughly maintaining significance throughout a computation. The more sophisticated scientific rules are known as propagation of uncertainty. Numbers are often rounded to avoid reporting insignificant figures. For example, it would create false precision to express a measurement as 12.34525 kg if the scale was only measured to the nearest gram. In this case, the significant figures are the first 5 digits from the left-most digit (1, 2, 3, 4, and 5), and the number needs to be rounded to the significant figures so that it will be 12.345 kg as the reliable value. Numbers can also be rounded merely for simplicity rather than to indicate a precision of measurement, for example, in order to make the numbers faster to pronounce in news broadcasts. Radix 10 (base-10, decimal numbers) is assumed in the following. Identifying significant figures Rules to identify significant figures in a number Note that identifying the significant figures in a number requires knowing which digits are reliable (e.g., by knowing the measurement or reporting resolution with which the number is obtained or processed) since only reliable digits can be significant; e.g., 3 and 4 in 0.00234 g are not significant if the measurable smallest weight is 0.001 g. Non-zero digits within the given measurement or reporting resolution are significant. 91 has two significant figures (9 and 1) if they are measurement-allowed digits. 123.45 has five significant digits (1, 2, 3, 4 and 5) if they are within the measurement resolution. If the resolution is 0.1, then the last digit 5 is not significant. Zeros between two significant non-zero digits are significant (significant trapped zeros). 101.12003 consists of eight significant figures if the resolution is to 0.00001. 125.340006 has seven significant figures if the resolution is to 0.0001: 1, 2, 5, 3, 4, 0, and 0. Zeros to the left