What is Fractional Share Investing?

What is Fractional Share Investing? Is this possible in India?

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Quantity less than 1 whole share is called fractional share, similar to piece of a pie. So, if a share is quoting 10,000 Rs or usd and one want to buy value worth 1000 then he will get .1(1/10) of that share.This is quite popular in US.
This is not allowed in India for various reasons, importantly in India all shares are traded in multiples of 1 on exchanges and trading should happen on exchange only but in US there is no need to send orders to exchange to get executed, orders can be diverted to darkpools, ECNs or broker can be counter party etc, so in these cases broker can hold few shares and be counter party to clients who want to execute fractional shares.

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How do they execute voting rights in case of fractional share holdings ?

Also , why not india follow the same trend like usa ?

No voting rights for them.

India is still a growing market, not matured enough as of USA, maybe something like that in distant future.