We round numbers if we only need a reasonable approximation rather than the exact value.
Rounding a number can be done:
 to a certain number of decimal places
 to a certain number of significant figures
 to the nearest whole number (or to the nearest ten, hundred, thousand etc.)
All rounding follows the same basic steps:
Example
Round these numbers to the specificed number of decimal places:
(a) 6.2348 to 2 decimal places
(b) 5.2718 to 3 decimal places
(1) First we place the cutoff point after the 2nd decimal place:
6 . 2 34 8
(2) The digit after the cutoff point is not 5 or more, so the digit before it is not changed:
6 . 2 34 8
(3) The digits after the cutoff point are removed:
6 . 2 3
(4) There are no gaps to fill between the cutoff point and the decimal point, so our answer is:
6 . 2 3 (2 d.p.)
(1) First we place the cutoff point after the 3rd decimal place:  5 . 2 7 18 
(2) The digit after the cutoff point is 5 or more, so the digit before it is increased by 1:  5 . 2 7 28 
(3) The digits after the cutoff point are removed:  5 . 2 7 2 
(4) There are no gaps to fill between the cutoff point and the decimal point, so our answer is:  5 . 2 7 2 (3 d.p.) 
Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Round 13.68952 to 1 decimal places
(b) Round 13.68952 to 3 decimal places
(c) Round 13.68952 to 4 decimal places
The diagram below shows the significant figures in the numbers 302.150 and 0.005106
Example
Round these numbers to the specificed number of significant figures:
(a) 523.591 to 4 significant figures
(b) 3441.5 to 2 significant figures
(1) First we place the cutoff point after the 4th significant figure:
5 2 3 . 59 1
(2) The digit after the cutoff point is 5 or more, so the digit before it is increased by 1:
5 2 3 . 69 1
(3) The digits after the cutoff point are removed:
5 2 3 . 6
(4) There are no gaps to fill between the cutoff point and the decimal point, so our answer is:
5 2 3 . 6 (4 s.f.)
(1) First we place the cutoff point after the 2nd significant figure:  3 44 1 . 5 
(2) The digit after the cutoff point is not 5 or more, so the digit before it is unchanged:  3 44 1 . 5 
(3) The digits after the cutoff point are removed (but not the decimal point):  3 4_ _ . _ 
(4) The gaps between the cutoff point and the decimal point are filled with zeroes, giving:  3 4 0 0 (2 s.f.) 
Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Round 3.642 to 2 significant figures
(b) Round 314769 to 3 significant figures
(c) Round 0.00723 to 1 significant figures
The diagram below shows the place values in the number 4892.1
Example
Round the number 4892.1 to the specificed accuracy:
(a) to the nearest 10
(b) to the nearest thousand
(1) First we place the cutoff point after the tens column:
4 8 92 . 1
(2) The digit after the cutoff point is not 5 or more, so the digit before it is unchanged:
4 8 92 . 1
(3) The digits after the cutoff point are removed:
4 8 9_ . _
(4) The gaps between the cutoff point and the decimal point are filled with zeroes, giving:
4 8 9 0 (nearest 10)
(1) First we place the cutoff point after the thousands column:  48 9 2 . 1 
(2) The digit after the cutoff point is 5 or more, so the digit before it is increased by 1:  58 9 2 . 1 
(3) The digits after the cutoff point are removed (but not the decimal point):  5_ _ _ . _ 
(4) The gaps between the cutoff point and the decimal point are filled with zeroes, giving:  5 0 0 0 (2 s.f.) 
Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Round 3647.5 to the nearest 10
(b) Round 3647.5 to the nearest 100
(c) Round 3647.5 to the nearest 1000
(d) Round 3647.5 to the nearest 1 (whole number)
