With three tokens in the hundreds place, four in the tens place and five in the ones place.
With four tokens in the hundreds place, nothing in the tens place and 2 in the ones place.
When the ancients wanted to write their numbers down they had to translate the number represented by the tokens into their more complicated ways of writing numbers. For example, they had no symbol to represent the nothing in the tens place of 402. In India the story was different.
It is difficult to say when writing a symbol as a place holder began. I wish I could write a post about the genius who did it, but so much of Indian mathematics has been lost down the memory hole due to the passage of time and colonialism. There is a vast amount of mathematics that was done in India that is only slowly being given credit in the west. Indian mathematicians had algorithms equivalent to Newton’s Method nearly a millennium before Sir Issac laid out his plan. They had a firm grasp of using infinite series to approximate the sine and cosine functions centuries before Europeans were doing the same thing.
The oldest surviving document of Indian mathematics is the Bakhshali Manuscript which has been dated ‘between 2nd century BC and 2nd century AD.’ The numerals used look like this:
Notice the dot used to represent zero. This is the earliest surviving example of a zero symbol. The title of the manuscript is not known though scholars agree that it is a compilation of earlier works of Indian mathematics, all of which are now lost.
Hopefully in the next few decades more information will surface that will demonstrate more of the beginnings of Indian mathematics.
Activity: Try to do multiplication with Roman numerals, without resorting to the familiar Hindu-Arabic number system.