How to plot extremely small numbers

Question

For example, I have a data set like the below:

Sequence: 1, 2, 3, 4, 5, 6, 7, 8; X: 0.5, 0.2e-5 , 0.2e-6, 0.2e-7, 0.2e-8, 0.2e-9, 0.2e-10, 0.2e-11;
Y: 0.6, 0.3e-4, 0.3e-5, 0.3e-6, 0.3e-7, 0.3e-8, 0.3e-9, 0.3e-10.

If I directly plot these data by sequence, we cannot see any difference between X and Y starting from sequence 2 because those numbers are so small.

Are there some plotting methods that can handle such small numbers? For example, I wish the plot has the Y-axis from 1 to 0.2e-12, and the width of Y-axis are the same for 1 to 0.1, 0.1 to 0.01, 0.01 to 0.001, etc. Basically, I hope the Y-axis can have different value magnitude, such that the number difference in small values can be highlighted well.

Thank you very much for your help.

Answer 1

Are there some plotting methods that can handle such small numbers? For example, I wish the plot has the Y-axis from 1 to 0.2e-12, and the width of Y-axis are the same for 1 to 0.1, 0.1 to 0.01, 0.01 to 0.001, etc.

This is called a logarithmic scale, or log plot, and is extremely common in scientific literature. Most data analysis programs should support this natively.

Answer 2

All the coordinates are positive.

Make a log log plot of the data to include all data.

If you leave out the first point $ (0.5,0.6)$ as already you know how big it is, (log x - log y) zooms to a better plot .. the range/domain scales -5 to -11 in the smaller magnitude region.