When an Offer is placed into an order book, its exchange rate is truncated based on the TickSize values set by the issuers of the currencies involved in the Offer. When a trader offers to exchange XRP and an issued currency, the TickSize from the issuer of the currency applies. When a trader offers to exchange two issued currencies, the offer uses the smaller TickSize value (that is, the one with fewer significant digits). If neither currency has a TickSize set, the default behavior applies.
The TickSize value truncates the number of significant digits in the exchange rate of an offer when it gets placed in an order book. Issuers can set TickSize to an integer from 3 to 15 using an AccountSet transaction. The exchange rate is represented as a number of significant digits plus an exponent; the TickSize does not affect the exponent. This allows the Ripple Consensus Ledger to represent exchange rates between assets that vary greatly in value (for example, a hyperinflated currency compared to a rare commodity). The lower the TickSize an issuer sets, the larger the increment traders must offer to be considered a higher exchange rate than the existing Offers.
The TickSize does not affect the portion of an Offer that can be executed immediately. (For that reason, OfferCreate transactions with tfImmediateOrCancel are unaffected by TickSize values.) If the Offer cannot be fully executed, the transaction processing engine calculates the exchange rate and truncates it based on TickSize. Then, the engine rounds the remaining amount of the Offer from the "less important" side to match the truncated exchange rate. For a default OfferCreate transaction (a "buy" Offer), the TakerGets amount (the amount being bought) gets rounded. If the tfSell flag is enabled (a "sell" Offer) the TakerPays amount (the amount being sold) gets rounded.
When an issuer enables, disables, or changes the TickSize, Offers that were placed under the previous setting are unaffected.
Since transactions can take time to propagate and confirm, the timestamp of a ledger is used to determine offer validity. An offer only expires when its Expiration time is before the most-recently validated ledger. In other words, an offer with an Expiration field is still considered "active" if its expiration time is later than the timestamp of the most-recently validated ledger, regardless of what your local clock says.
You can determine the final disposition of an offer with an Expiration as soon as you see a fully-validated ledger with a close time equal to or greater than the expiration time.