Here's an excerpt from Michael Lewis's Flash Boys book:
Part of that narrowing would have happened anyway, with the automation of the stock market, which made it easier to trade stocks priced in decimals rather than in fractions.
Could you please explain "in decimals" and "in fractions"?
It means whether the prices at which trading can occur at the exchange end in fractions or in decimals after the whole number part (e.g. $32¼ or $32.25). It used to be fractions of the currency, specifically with some pre-determined minimum spacing between nearest possible values (usually in base 2, with halves, quarters, eighths, sixteenths of e.g. 1 USD or 1 GBP), and it was changed to fractions of base 10, again with some pre-determined minimum spacing between nearest possible values.
But the change was usually such that the difference between the two nearest base-10 fractions was smaller than between the two nearest base-2 fractions, allowing for smaller steps in asset prices. If you assume that the asset has an underlying price which may be not exactly any allowed trading price, and which is approximated by the fractions at which trading is allowed, then tighter (smaller) differences between the two nearest allowed prices is beneficial as it allows the trading price to be closer to the underlying price.
According to Wikipedia, the New York Stock Exchange used fractions until 2001:
In 2001, trading in fractions (n⁄16) ends, replaced by decimals (increments of $0.01, see Decimalization)
You can see that 0.01<1⁄16 (because 1⁄16=0.0625), so 0.01 is preferable as it allows more accurate price finding.
