A significant figure shows the number of figures we have confidence in.A figure becomes significant or important if is accurately known.

Rule 1:All non-zero figures are significant.

Rule 2:In case of whole numbers, the zeroes at last are significant or not significant according to the accuracy of the experiment.Hence such zeroes are known as ambiguous zeroes.

Eg;Mass of body=9800g

last 2 zeroes are significant, if accuracy of experiment is 1g.

last 1 zero is significant, if accuracy of experiment is 10g.

no zero is significant if accuracy of expt. is 100g.

Rule 3:In case of decimal numbers, zeroes at the end is significant.

Rule 4:In case of pure decimal numbers, the zeroes between decimal point and the first non-zero digit are not significant.

Eg;0.0027-only 2 s.f.

Rule 5:Zeroes btw 2 significant figures are significant.

Eg;0.00207- 3 s.f.

Rule 6:Number of significant figures is independent of unit.

Rule 7:In case of accurately known nos. the number of significant figures is infinite.

Eg;A cube has 6 sides.6 is accurately known.

No.of significant figures= infinite

Rule 8:Rule for multiplication and division

The no. of s.f in the result is equal to the min. no. of significant figures in the components.

Rule 9:Rule for addition and subtraction

The result will have as many decimal places as the min. no. of decimal places in the component.

The rule of rounding up implies only when the figure dropped is 5 followed by all zeroes or nothing(i.e. the rule -when figure in front of 5 is odd,add one; and if even, leave it as such).

Here the sum of all given digits provides answer 796.53.By rule for addition, the least number of decimal places is of 756(no decimal places) and so it must be rounded as 797 as 5 is followed by 3.(rule of rounding does not imply in this situation)