Question

In the number 548, which is the least and most significant digits? Also write the positional value of number 5.

Answer 1

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Explanation:

The significant figures (also known as the significant digits or precision) of a number are digits that carry meaningful contributions to its measurement resolution. This includes all digits except:[1]

All leading zeros. For example, "013." has two significant figures: 1 and 3;

Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures); and

Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.

Of the significant figures in a number, the most significant is the position with the highest exponent value (the left-most in normal decimal notation), and the least significant is the position with the lowest exponent value (the right-most in normal decimal notation). 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 (which has seven significant figures) if the scales only measured to the nearest gram and gave a reading of 12.345 kg (which has five significant figures). Numbers can also be rounded merely for simplicity rather than to indicate a given precision of measurement, for example, to make them faster to pronounce in news broadcasts.