Question 9 - Figure it out - Page 44, 45 - Chapter 2 Class 8 - Power Play (Ganita Prakash)

Transcript

Question 9 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?Billion has 9 zeros Thus, 8.5 billion = 8.5 × 109 Since we can use digits 0-9, it means we have 10 digits for each position We need to find number of digits the code should consist of If we create a 2-digit code Number of IDs it can make = 10 × 10 = 102 If we create a 3-digit code Number of IDs it can make = 10 × 10 × 10 = 103 Similarly, If we create a 9-digit code Number of IDs it can make = 109 But, 109 < 8.5 × 109 So, we need a 10-digit code Creating a 10-digit code Number of IDs it can make = 1010 Since 1010 > 8.5 × 109 We have enough IDs now. Thus, we need a 10-digit code