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On graphic scales (as seen below), why isn’t "0" at the far left of the scale?

1 Answer

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Final answer:

Zero is not at the far left of logarithmic scales because the logarithms of non-positive numbers are undefined, meaning zero falls at negative infinity, which is not representable on a finite graph. Logarithmic scales are employed to represent wide-ranging data in a manageable form, with each increment indicating a multiplicative increase.

Step-by-step explanation:

The question pertains to why '0' is not at the far left of the graphic scale depicted in the examples provided. The primary reason is that the scales referenced are logarithmic scales, which are used to represent data that cover a wide range of values. On a logarithmic scale, each increment indicates an increase by a constant factor, commonly a factor of ten. This effectively allows for a concise graphical representation of large differences. Zero cannot be placed on a logarithmic scale because logarithms of non-positive numbers are undefined; thus, zero would theoretically lie at negative infinity on such a scale, making it impossible to include on a finite graph.

Furthermore, when choosing scales for axes on graphs (vertical or horizontal), the goal is to show all the data and easily identify trends. Depending on whether the scale is made larger or smaller, the perceived trend and magnitude of fluctuation can be greatly affected. A scale needs to be selected meticulously to present the data as accurately and clearly as possible without distorting the perception of its variability or significance.

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