9
Question A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each packet. If they choose to use the digits 0-9, how many digits should the code consist of?
Total no. of packets produced in a year = 8.5 billion ∴ Number of codes required = 8.5 × 10 9 codes For ID digits to be taken from 0 to 9. So each digit has 10 choices. To make code with n digits, the total number of possible codes = 10 n ∴ 10 n ≥ 8.5 × 10 9 10 9 = 1,00,00,00,000 The smallest value of n that satisfies 10 n ≥ 8.5 × 10 9 is 10. Hence number of digits the code should consist of 10 10 .