17/06/2024
WILL WE EVER RUN OUT OF BARCODES?
This was a question posed to me by one of my year 11 students in the run up to her final exams. I then examined her water bottle, which unsurprisingly contained a barcode, which is an unsung hero of modern technology which makes retail transactions seamless. The bar code on this girl’s water bottle provided fertile ground for mathematical discussion and analysis.
The mathematical tool used here is the product rule for counting, a topic on the current GCSE syllabus. To introduce the topic, I could ask how many two-digit numbers are possible to make? To make the first digit, there are 10 digits from zero to nine to choose from. Likewise, to make the second digit, there is the same choice of 10 digits. So the total possible quantity of two-digit numbers (00 through to 99) can be arrived at by calculating 10 x 10 = 100.
Back to barcodes. There are 13 digits on a standard barcode, which means there are 10 to the power 13 possible barcodes available. That is 1 followed by 13 zeros, or ten trillion. Now as of June 2024, there are just over 8 billion people in the world. This allows for a maximum of 1250 unique products for every man, woman and child on this planet. Despite capitalism being the dominant system that runs our world today, I don’t think there are 10 trillion unique products or indeed that anybody owns anywhere near a thousand unique products, so it is safe to say we will not run out of barcodes any time soon.
*Image obtained from the back of my son’s 6th birthday card. If this post interests you, please write a comment below!