Example
Density = Mass / Volume
if mass = 4.237 g ( 4 significant figures ) and Volume = 2.51 cm 3 ( 3 significant figures )
Density = 4.237 g / 2.51 cm 3 = 1.68804 g cm -
3
= 1.69 g cm -3 ( 3 significant figures )
Addition of
436.32 ( 2 digits after decimal ),
227.2 ( 1 digit after decimal ) & . 301 ( 3 digits after decimal ) is
= 663.821
Since 227.2 is precise up to only 1 decimal place , Hence , the final result should be 663.8
Rules for Rounding off the uncertain digits
Rounding off is necessary to reduce the number of insignificant figures to adhere to the rules of arithmetic operation with significant figures .
Rule Number |
Insignificant Digit |
Preceding Digit |
Example ( rounding off to two decimal places ) |
1 |
Insignificant digit to be dropped is more than 5 |
Preceding digit is raised by 1 . |
Number – 3.137
Result – 3.14
|
2 |
Insignificant digit to be dropped is less than 5 |
Preceding digit is left unchanged . |
Number – 3.132
Result – 3.13
|