Calculate the answer up to appropriate numbers of significant digits 
(a) The ratio of the mass of proton 'mₚ' to the mass of electron 'mₑ' 

`\frac {mₚ}{mₑ}` = `\frac {1.67 x 10⁻²⁷ kg}{9.1096 x 10⁻³¹ kg}`

(b) The ratio of the charge on electron 'qₑ' to a mass of electron 'mₑ' 

`\frac {qₑ}{mₑ}` = `\frac {1.6 x 10⁻¹⁹ C}{9.1096 x 10⁻³¹ kg}`


Solution:

(a) The ratio of the mass of proton 'mₚ' to the mass of electron 'mₑ' .

As Given

`\frac {mₚ}{mₑ}` = `\frac {1.67 x 10⁻²⁷ kg}{9.1096 x 10⁻³¹ kg}`
by simplifying

`\frac {mₚ}{mₑ}` = `\frac {1.67}{9.1096}` x 10⁻²⁷⁺³¹

`\frac {mₚ}{mₑ}` = 0.183 x 10⁴

According to the rules of significant figures, when quantities are multiplied or divided, the result has the same significant figures as the quantity with the smallest numbers of significant figures. In the given numbers, 1.67 x 10⁻²⁷ kg has the lowest 3 significant digits. So, the result of the calculation should be rounded to three significant digits. Here We have

`\frac {mₚ}{mₑ}` = 0.183 x 10⁴ 

`\frac {mₚ}{mₑ}` =  1.83 x 10³    -------Ans.   

(b) The ratio of the charge on electron 'qₑ' to the mass of electron 'mₑ' 


`\frac {qₑ}{mₑ}` = `\frac {1.6 x 10⁻¹⁹ C}{9.1096 x 10⁻³¹ kg}`

`\frac {mₚ}{mₑ}` = `\frac {1.6}{9.1096}` x 10⁻¹⁹⁺³¹

`\frac {mₚ}{mₑ}` = 0.1756 x 10¹²

According to the rules of significant figures, when quantities are multiplied or divided, the result has the same of significant figures as the quantity with the smallest number of significant figures. In the given numbers, 1.6 x 10⁻¹⁹ kg has the lowest 2 significant digits. So, in the result of the calculation should be rounded to two significant digits. Here We have

`\frac {qₑ}{mₑ}` = 0.1756 x 10¹² 

`\frac {qₑ}{mₑ}` = 1.8 x 10¹¹    -------Ans.   


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