12. CBQ - Number systems

4 m.

An engineer is comparing ancient record-keeping methods. He finds a record of '1900' written in three different ways:

(a) 19 'hundred' symbols, (b) '\(\text{MDCCCC}\)' in Roman numerals, and (c) '1900' in modern digits.

1. Which system is the most 'scalable' for recording much larger numbers like \(2,400,000\)?

2. In the modern representation '1900', what is the mathematical role of the two zeros?

They act as placeholders to ensure the \('1'\) and \('9'\) stay in the thousands and hundreds places.
They indicate that the number is a whole number.
They are decorative and don't change the value of the \(19\).
They represent a value of \(10\) each

3. If the engineer tried to multiply '\(\text{MDCCCC}\)' \(1900\) by 'X' \(10\) using Roman rules, why would it be difficult?

The system lacks a consistent way to 'carry over' values between places like ones, tens, and hundreds.
The symbols are too hard to write.
Multiplication wasn't invented when Romans were alive.
Roman numerals can only represent odd numbers

4. Comparing 'Efficiency', how many symbols are used to write \(3,888\) in Roman vs. Hindu-Arabic?

Did you find an error?