# Correcting to 3 decimal places (3 d.p) and to 3 significant figures (3 s.f)

• Jan 4th 2011, 12:48 PM
SWEngineer
Correcting to 3 decimal places (3 d.p) and to 3 significant figures (3 s.f)
In correcting this number: "0.39" to 3 d.p and 3 s.f, would it be as follows?

3 d.p --> 0.390
3 s.f --> 0.390

Thanks.
• Jan 4th 2011, 12:52 PM
rtblue
Yes, you are correct.

For any further questions on significant digits, try this website:

Significant Figures
• Jan 4th 2011, 12:54 PM
pickslides
Quote:

Originally Posted by SWEngineer

3 s.f --> 0.390

Thanks.

There are only two significant figures here as the number can be written as .39
• Jan 4th 2011, 12:57 PM
rtblue
0.39 can also be expressed as $\displaystyle 3.90*10^{-1}$, in which case there are three significant digits.
• Jan 4th 2011, 12:58 PM
SWEngineer
But, even that the last zero can be ommited after the decimal place, we are asked here for 3 s.f, which means there should be three numbers.

For example, what is the solution for this question:

Correct 0.0004298 to 3 s.f? When you solve it you will know what I mean.

Thanks.
• Jan 4th 2011, 12:59 PM
rtblue
0.0004298 to 3 significant figures would be 0.000430
• Jan 4th 2011, 01:01 PM
SWEngineer
Quote:

Originally Posted by rtblue
0.0004298 to 3 significant figures would be 0.000430

Yes, this is what I was trying to tell @pickslides
• Jan 4th 2011, 03:54 PM
HallsofIvy
Quote:

Originally Posted by SWEngineer
But, even that the last zero can be ommited after the decimal place, we are asked here for 3 s.f, which means there should be three numbers.

Yes, because the number of "significant digits" tells you the accuracy of the measurement. 0.39 means that, measured to the nearest hundreth, the number is 0.39- that is that the true value is somewhere between 0.385 and 0.395. 0.390 means that it was measured to thousandths place- the true value is between 0.3995 and 0.3905.

Quote:

For example, what is the solution for this question:

Correct 0.0004298 to 3 s.f? When you solve it you will know what I mean.

Thanks.
0.0004298 to 3 significant figures is 0.000430 or, better, $\displaystyle 4.30 \times 10^{-4}$. The fact that it has 3 significant figures means it is accurate to between 0.0004295 and 0.0004305.
• Jan 8th 2011, 11:22 PM
SWEngineer
Thanks a lot for your replies.