Question

Rules of significant figures

Answer 1

There are three rules on determining how many significant figures are in a number:

1)Non-zero digits are always significant.
2)Any zeros between two significant digits are significant.
3)A final zero or trailing zeros in the decimal portion ONLY 

Answer 2

$Here \: is \: the \: answer \: of \: your \: question$

`$\textbf{Significant Figure}$`

The total number of digits in a number including the last digit whose value is uncertain is known as Significant Figure.
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`$\textbf{Rules for determining the number of Significant Figures}$`

1) All non zero digits as well as zero between the non zero digits are significant.
Ex :-
1008 = 4 significant figure
1080 = 3 significant figure
0180 = 2 significant figure

2) In case all number having Decimal.

a) Zeros to the left of first non zero digit are non significant
Ex :-
0.0018 = 2 significant figure

b) If a number ends in zero which are to the right of the decimal point are significant.
Ex :-
1800.0 = 5 significant figure
0.01300 = 4 significant figure

3) If a number without decimal ends in zero then zero may or may not be significant. It depends upon the way of representation.
Ex :-
1.800 × 10³ = 4 significant figure
1.80 × 10³ = 3 significant figure
1.8 × 10³ = 2 significant figure
1.0 × 10³ = 2 significant figure

4) Rounding off of figures
Ex :-
6.324535 × 10² = 8 significant figure
6.32453 × 10² = 6 significant figure
6.3 × 10² = 2 significant figure

→ During Addition and subtraction significant figure has no rule to play. Result should be report up to one decimal place.
Ex :-
4.5326 + 12.83 + 5.6 = 22.9626
Now, shortest is 5.6 means (in 2 s.f.)
So, answer is 23.0 (in 2 s.f.)

→ During multiplication and division result should have least number of significant figures.
Ex :-
6.25 × 2.5 = 18.625 have 5 significant figure
= 18.63
= 18.6
= 19.0 have 2 significant figure
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