Please correct me if I’m wrong, but I’ve read that the reason why we use significant figures is to avoid making the result of a calculation more accurate than the starting values prior to the calculation. For example, if we were seeking the ratio of two weights, lets call them A and B, using a cheap scale and an expensive scale we could get the following varied results:
Cheap Scale $$A = 34 \space oz$$ $$B = 23 \space oz$$
Expensive Scale $$A = 34.0000 \space oz$$ $$B = 23.0000 \space oz$$
Computing the ratio $\frac{A}{B}$ using a calculator we get the following value: $$\frac{34}{23} = 1.47826$$ Now this is a correct ratio depending on the scale used (ie the cheap scale could not have produced such an accurate measurement given the starting values) This leads to the following question:
Why are the zeros behind a decimal point ignored if they are just place holders?
For example, the value 0.000023 oz only has two significant figures, but isn’t that value something only a very fine tuned scale could measure (keeping in line with the previous weight example). So why are these zeros ignored?