Express the results of the following calculations to the appropriate number of significant figures :
(i) `(3.24 xx 0.08666)/5.006`
(ii) `((1.36 xx 10^(-4))(0.5))/2.6`
(iii) `0.582 + 324.65`
(iv) `2.64 xx 10^(3) + 3.27 xx 10^(2)`
(v) `943 xx 0.00345 + 101`.

Explanation

(i) `(3.24 xx 0.08666)/5.006 =0.05608 = 0.0561`
In the calculation, the number of significant figures in the term 3.24 is 3, therefore, the result should have 3 significant figures. Therefore, the correct answer is 0.0561. The number after 0 is 8 and therefore it is rounded off to 1.
(ii) `((1.36 xx 10^(-4))(0.5))/2.6 = 0.2615 xx 10^(-4)`
`=0.3 xx 10^(-4)`
The answer should have one significant figure because 0.5 has one significant figure.
(iii) `0.582 + 324.65 = 325.232`
Since 324.65 contains digits up to second place of decimal, therefore, the answer must be reported up to second place.
(iv) `2.64 xx 10^(3) + 3.27 xx 10^(2)`
Since 2.64 has two digits after decimal place, the answer should be rounded off to two decimal places.
(v) The first two numbers are to be multiplied initially as follows:
`943 xx 0.00345 = 3.25335=3.25`
According to the rules on multiplication of significant figures, the answer has to be reported up to three significant figures. It should be 3.25. Upon further addition, the final answer may be calculated as :
`3.25 + 104.25=104`
The answer should have zero place of decimal