Modelling number quantities up to 2,450,000
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It's not clear what you're asking for, so I'm going to guess that you want to scale numerical quantities up to 2450000 on a graph.

There are two ways you might do this: linear or logarithmic.

LINEAR

In this representation, the quantities need to be scaled down to fit on to graph paper. Let's assume that all quantities are positive and we are using A4-sized paper. A4 is 210mm by 297mm, usually marked with 1cm divisions and 1mm subdivisions. If both axes are to accommodate the maximum quantity, then different scaling is needed for each axis. Let's start with the shorter axis, then 1mm would represent 11667, which is an awkward number to deal with, so let's choose an easier representation, for example, 1mm=12500, so 8mm (0.8cm) would represent 100000. If 8mm is used as the major division, the mm subdivisions would be 1mm=12500, 2mm=25000, 3mm=37500, 4mm=50000, 5mm=62500, 6mm=75000, 7mm=87500. The main divisions should be marked and labelled 100000, 200000, 300000, ..., 2600000 at 0.8cm, 1.6cm, 2.4cm, ..., 20.8cm. You could use the labels 100k, 200k, 300k, etc., or even 1, 2, 3, etc. (representing 1×105, 2×105, etc.) to shorten the labels conveniently. In this representational scaling 2,450,000 would lie midway between the 24th and 25th main division.

The longer axis could use the scaling 1mm=10000. 10mm would represent 100000. Label the main divisions (each cm) 100000, 200000, 300000, etc. Again the label names can be shortened. In this representational scaling 2,450,000 would also lie midway between the 24th and 25th main division.

The shorter axis would accommodate numbers up to 2,625,000 and the longer axis up to 2,970,000.

These axes easily accommodate the requirements.

Representing a number like 1,234,567 would mean the loss of resolution because it needs to be expressed as a multiple of 12500. This is about 99 mm subdivisions, or a little more than 1,200,000 (1200k). The remainder 34,567 is a little under 3 mm subdivisions further along the axis, that is, just under a third the distance between 1200k and 1300k. So the graph is low resolution.

LOGARITHMIC

For some applications it may be better to represent quantities by using their logarithms, usually to base 10. The number 0 can't be represented this way, but all natural numbers can (1, 2, 3, ...). log10(1)=0, log10(10)=1, log10(100)=2, ..., log10(2450000)=6.39 approx, so plotting the logs greatly reduces the scale. The disadvantage is the inconvenience of having to calculate the logs before plotting.

I hope this helps.

by Top Rated User (1.1m points)

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