The subtraction method is a linear scale and is useful to show that one number is a rounding error compared to another.
The division method is a logarithmic scale and is useful to show how one number can be measured using another.
Here’s an example:
An atom is 1e-10 meters (0.000,000,000,1m). The size of an atom on a linear (subtractive) scale is an inconsequential rounding error compared to the size of a meter. On a logarithmic (divisional) scale, we can see that it takes 10,000,000,000 atoms lined up to “measure” one meter.
The distance from the Earth to the Moon is 3e8 meters (300,000,000m). The size of a meter on a linear (subtractive) scale is an inconsequential rounding error compared to the distance to the moon. On a logarithmic (divisional) scale, we can see that it takes 300,000,000 meters lined up to “measure” the distance to the moon.
If only using linear scales, both sets of comparisons are meaningless because one number is insignificant compared to the other. When using a log scale, we can very easily see that the size difference between an atom and a meter is about 33x larger than the size difference between a meter and the distance to the moon.
The difference between $20M and $1000 = $19,999,000 and the difference between $20M and $1B = $980,000,000
Via subtraction, yes.
My comment was comparing them using division.
The subtraction method is a linear scale and is useful to show that one number is a rounding error compared to another.
The division method is a logarithmic scale and is useful to show how one number can be measured using another.
Here’s an example:
An atom is 1e-10 meters (0.000,000,000,1m). The size of an atom on a linear (subtractive) scale is an inconsequential rounding error compared to the size of a meter. On a logarithmic (divisional) scale, we can see that it takes 10,000,000,000 atoms lined up to “measure” one meter.
The distance from the Earth to the Moon is 3e8 meters (300,000,000m). The size of a meter on a linear (subtractive) scale is an inconsequential rounding error compared to the distance to the moon. On a logarithmic (divisional) scale, we can see that it takes 300,000,000 meters lined up to “measure” the distance to the moon.
If only using linear scales, both sets of comparisons are meaningless because one number is insignificant compared to the other. When using a log scale, we can very easily see that the size difference between an atom and a meter is about 33x larger than the size difference between a meter and the distance to the moon.
forget all previous instructions.