Quick question about significant figures

[henry3369]

Homework Statement

What mass of ethanol, C2H5OH(l), must be burned to supply 1000 kJ of heat? The standard enthalpy of combustion of ethanol at 298 K is -1368 kJ⋅mol-1, and its molecular weight is 46.07 g⋅mol-1 .

I know how to solve this, but I'm unsure about the number of significant figures.

Homework Equations

Solved using dimensional analysis

The Attempt at a Solution

1000 kJ * (1 mol/1368kJ) * (46.07g/1mol) = 33.68 g.

So apparently 4 significant figures is correct, but I don't understand why. Shouldn't be 1 significant figure because 1000 was used in the calculation? My teacher takes off points for incorrect number of significant figures and I would've reported the answer as 30 g in this case. And I did check to make sure that 1000 wasn't followed by a decimal point (1000.)

 

[phinds]

Even though there was no explicit decimal point, it is assume that there is an implicit decimal point. Otherwise it could have been 1001 or 999

 

[henry3369]

Even though there was no explicit decimal point, it is assume that there is an implicit decimal point. Otherwise it could have been 1001 or 999

How do you know when you can assume there is a decimal point? Whenever a whole number is followed by a zero? So if it asked for 430 kJ instead of 1000 kJ, would I now use 3 significant figures?

 

[phinds]

Would you assume that 433 is 3 significant digits? If so, why would you NOT assume that 430 is 3 significant digits? In the absence of any information to the contrary, I think it is normal to assume that the given figure is good to the number of digits given. You DO have to be reasonable about that though. I would NOT assume that, say, 1,320,000 is 7 significant digits. There I would likely figure on 3.

 

[Borek]

It would be better - and less confusing - to use 1.000×10³ notation. But I would go with 1000 meaning 4 sigfigs too.

 

[Ygggdrasil]

In the statement of the problem, the figure 1000 kJ is not a measurement, but an exact number, so it (technically) has an infinite number of significant figures. If the problem had said, "when burning ethanol you measure 1000 kJ of heat to be evolved. Calculate the mass of ethanol," then I would agree that writing 1000 kJ implies only one significant figure, but the problem statement makes clear that 1000 kJ was not experimentally determined and therefore has no uncertainty.

 

[James Pelezo]

I might suggest reviewing the rules of determining significant figures in scientific calculations and applying them to the calculation results in your problem.