# Significant figures in conversion factors?

Example: I have $\pu{64 cm^{3}}$ of milk. How much is that in gallons?

When I use the conversion factors $\frac{\pu{1 mL}}{\pu{1 cm^3}}$ $\frac{\pu{1L}}{\pu{1000 mL}}$ $\frac{\pu{1.0567 qt}}{\pu{1 L}}$ $\frac{\pu{1 gal}}{\pu{4 qt}}$.

I know the final answer should only have two significant figures, but how many significant figures should the intermediate conversion factors have?

I have heard that:

• conversion factors should have one more sig fig than the least precise measurement. (So three in this case)

• But I also heard that we shouldn't round anything until the end. (So use all 5, and round after conversions are complete)

The reason why I got confused is because of my textbook:

• check your conversion factor. $1 \text{cm}^3$ is a milliliter which is much much less than a quart. – MaxW Sep 14 '16 at 20:14
• With a modern calculator, I wouldn't round anything until the end. When doing calculations with a slide rule or log tables, then things were a bit different. – MaxW Sep 14 '16 at 20:15
• This is case dependent. You need to realize what kind of mathematical object are you deal with. – user1420303 Sep 14 '16 at 20:52
• @MaxW, so is my textbook wrong in rounding in this example? – eromod Sep 15 '16 at 23:28
• As I said, if I had a calculator, I wouldn't round anything until the end. If I had to do all the calculations by hand, then I'd be inclined to round intermediate values. I'm not going to multiple two 8-digit numbers by hand and then round to 2 digits. – MaxW Sep 16 '16 at 3:36

• So if my measured quantity is $\ 64 cm^{3}$ , how many significant figures should I use in the qt/L conversion? All of them because its an exact conversion? Or just three sig figs (one more that the two I have to work with) – eromod Sep 15 '16 at 3:27