# Accuracy

 From: Tony Straw Date: 20 February 1999 Subject: Difference between d.p. and s.f. Please can you explain the difference between 3dp and 3sf?

### Maths Help suggests:

They are both ways of "rounding" the final answer of a calculation.

3dp means give the answer accurate to 3 decimal places.
So count up to the third digit after the decimal point, and ignore any digits after that.
For example:

12.56329 to 3dp = 12.563
Remember that if the first digit that you ignore is 5 or bigger, then you need to round up.
For example:
3.141592 to 3dp = 3.142
2.71828 to 3dp = 2.718
0.03875 to 3dp = 0.039
0.6799 to 3dp = 0.680 ..........a tricky one!

3sf means give the answer to three significant figures.
Remember that a "tail" of zeros (for big numbers) or a "lead-in" of zeros (for small decimal numbers) are not counted as significant.
For example: 1500 as it stands has 2 sig figs. 0.0001875 has 4 sig figs.

To round a number to 3sf, count off the first three significant figures. All other digits drop down to zero. As before, if the first digit you lose is 5 or more, you need to round up.
For example:

2573490 to 3sf = 2570000
98765 to 3sf = 98800
10069 to 3sf = 10100 ..........Note that zeros within the number are counted as significant

0.0012345 to 3sf = 0.0012300 = 0.00123 (since a tail of zeros at the end of a decimal are unnecessary)
0.08759 to 3sf = 0.08760 = 0.0876