Sig figs and exact numbers

Question

I have a question about sig figs and decimals. If you start off with an exact value like 8.00 m which is 3 sig fig and you multiply by 100 cm so 800 cm. Then you divide by 2.54 cm and get 314.96 in. Because it's 3 sig fig you round to get 315 inch my question is do you still place a decimal to get 315. Inch Or is it just 315 inch with no decimal. I am confused because by dividing by 2.54 cm and rounding it's no longer exact right? But you started off with an exact value of 8.00 m so does that make 315. Inch ?

Any pointers will help. Thanks.

Answer 1

If you start with just 8 it has infine significant figures. But 8.00 has exactly 3 significant figures. It's a common to get in chaos so we generally follow something different. Instead of writing 315 or 315. We follow 3.15 ×$10^2$ . So it has 3 significant numbers and less confusion.

we generally write one digit before decimal(from 1 to 9) and latter according to no. Of significant numbers.

$10^2$ doesn't count for significant digits.

Answer 2

It sounds like you are muddling up the difference between an exact value and a measurement.

$8.00$ is not an exact value unless it is a constant from a formula. If you got the value of $8.00$ from an experiment it means that you measured $8.00\pm0.005$ and it is not exactly the same as the integer $8$.

Similarly was the value $100$ from a formula (converting to a percentage maybe) or a measurement? And was $2.54$ a measurement or from a formula? If its the conversion from centimetres to inches then its a precise constant and has no error.

If the final value of $314.96$ resulted from some measurement in the calculation stesp then yes should have the answer of $315$ which is meaning $315\pm0.05$. You sound worried that people may think that it is an exact value as it has no decimal point. The fact it is a calculated value should be apparent from the words you use around it. If there is doubt you could write it as $315\pm0.5$ or as $3.15\times10^2$ or as $(3.15\pm0.005)\times10^2$.