# 7.05 Rounding values

## Problems with digits generated by calculations

Rule 1 states from the section on significant figures states All non-zero digits are considered significant (1,2,3,4,5,6,7,8,9). However calculations performed on measurement values can produce extra digits in the answers. These extra digits should not be recorded as this would imply increased precision (i.e. they should not be treated as significant digits). The values should be rounded up or down to an appropriate number of significant figures.

## Rounding numbers

The procedure for rounding a number off is as follows. If the digit after the last significant digit is less than five the value is rounded down so you simply discard all of the digits after the last significant figure. If the digit after the last significant figure is five or greater you round the value up. So the extra digits are discarded as before but the value of the last significant digit is increased by 1.

e.g.
1.37548 rounded to 4 significant figures is 1.375 (the uncertainty is +/- 0.0005)
1.37572 rounded to 4 significant figures is 1.376 (the uncertainty is +/- 0.0005)