Apple released the new iOS 9 last week, and if you have an iPhone or iPad, it's statistically likely you've already upgraded to the latest mobile OS: The Cupertino giant announced on Monday that more than half of Apple devices had already adopted iOS 9 in the few days after its Sept. 16 release date.

So this week, we present a special OS-edition of Tap That App, with our favorite new features to help you explore and get the most out of the new iOS 9. We'll be talking about apps, too.

First And Foremost: iOS 9 is Small

Of course, if you're in the minority of Apple users that haven't adopted the new operating system -- perhaps because you think you might not have enough space for it on your 16GB iPhone -- this year, there's (literally) less to worry about.

Unlike previous iOS updates, especially the over 4.5GB behemoth that was iOS 8, the new iOS 9 only takes up 1.3GB of space to install.

Even if you get the "Insufficient Space for Download" message after trying to grab the update, there's still hope in the form of a new button (below "cancel") at the bottom of that prompt: "Allow App Deletion."

Don't worry, you won't lose your favorite apps. Instead, Apple created an automatic app deletion and, more importantly, reinstallation feature. It's an easy, automatic way to free up some of your storage and you'll get your temporarily deleted apps right back.

Biggest Change: Smarter Siri and Search

While you won't notice much of a difference on the graphical face of iOS 9, the way iOS 7 shook up the old rounded icon aesthetic and color scheme, the biggest improvement in the update is a substantial one: Siri is smarter. And so is Search.

Apple's virtual assistant has always had the gift for gab, but in iOS 9 she's also beginning to act more like an assistant and less like a talkative bot that searches the web on command.

Apple has built in much more contextual awareness so that Siri can better understand what you need, when you need it, a la Google Now. For example, you can ask Siri to remind you of something while you're in an app, like Safari, in completely natural language without having to specify what exactly you're talking about. But you can also ask for more specific things, as well, like for Siri to bring up photos from a date or place.

Also like Google Now, Siri will observe your digital habits and begin brining up suggestions for apps and contacts when she thinks you might want them in the Siri Suggestions feature.

Finally, on the new iPhone 6s and 6s Plus, you can set Siri to always be listening for your command without needing to hit any buttons, with the "Hey Siri" feature. That brings the latest iPhones up to date with the Moto X 2013. But of course, with an older iPhone, you can already use "Hey Siri," but only if the iPhone is connected to a power source.

Spotlight Search

A smarter Siri is great, but perhaps the most useful big improvement on the day-to-day is Spotlight search, unless you're one of those iPhone people who constantly talk to Siri.

Once an oft-neglected little pane in the older iOS versions, Apple has drastically improved and obviously re-emphasized Spotlight search in iOS 9.

That's largely because Apple has empowered developers to tie their apps into Spotlight, providing deep searches into not only Apple's apps and contacts, but pretty much the entire phone.

Search has also been tied into Siri's brain, so the same commands, plain-language queries, and bonus features like a built-in instant calculator. And more types of searches bring up instant actionable items right in the results, like the phone and messaging button when you search for a contact.

New (or Improved) Apple Apps

Every iOS update comes with a laundry list of small changes to Apple's default apps, so here's the short count of the biggest ones.

News

Brand new to Apple, iOS 9 comes with an Apple-supported news app called, well, News. It's not the most amazing mobile news app out there -- Flipboard, which News looks and acts a lot like, still probably takes the cake -- but it is a brand new app that you'll find after you update.

Like other news apps, you can pick and chose topics and news outlets that you prefer, and optimize the selection as you go along. You can also share articles you like or set them aside so you can read them offline.

Notes

Notes may be the least-used default Apple app for me, but it may get a lot more attention after this update. That's because Notes now works with the share option, making it much more like an Evernote-style app in which you can easily save documents, web URLs, and unexpected things like from Apple Maps. You can also take photos directly from within Notes now.

But most importantly, you can scribble freehand notes with your finger now -- no Pencil and iPad Pro needed. Instead, Notes provides a graphical set of tools, including a ballpoint and felt-tip pen, and a pencil. Just select and doodle away!

Podcasts and Maps

A lot of people still use the default Podcasts app, despite a plethora of superior third-party options. It just got a little better with the iOS 9 update, though, as there's finally a tab for "Unplayed.'

Fewer people use Apple Maps, because "Google." But Maps also comes with a small update that improves directions for anyone that lives in a major city in the U.S. or across the world: transit directions.

Now you can use Apple Maps to get to the right subway, bus, or train in over 300 cities in China, major metropolitan hubs like Berlin, Tokyo, and London -- along with San Francisco (of course), New York, Washington D.C., Philaelphia, Chicago, and Baltimore in the U.S.

Apple remains "the little cartographer that could" and while Maps is still inferior to Google's offering, it's interesting to see the Cupertino company continue to grind away at improving Maps.

It's the Little Things

Apple has fed my obsession with tiny conveniences in technology with a few notable changes above and below the hood.

First, there's the new keyboard. Apple has made a full change in the system font in iOS 9, for the first time since iOS was introduced with the iPhone (1). It's gone from Helvetica Neue (a thinner version of the original Helvetica) to San Francisco, the original Apple font hand-made for the Watch.

It looks good on the keyboard, especially with the other big change: upper and lower case letters and a clearer shift key. This is something I always thought Android got right and could not stand with Apple. It just makes sense to be able to look at the keyboard and know whether you're about to type a capital letter or not.

Another annoying Apple keyboard legacy that is gone by default now is the pop-up letter animations that happen when you type. Fear not, Apple traditionalists: you can still turn those animations back on in the Settings app, along with the all-caps keyboard if you so bafflingly desire.

The second big/little change is below the screen, in the guts of iOS 9. It also happens to be a feature Android got to first: low power mode. In the Settings app, there's an option in the "Battery" menu for this that can help extend the tiny daily lifespan of your iPhone. It'll stop some background processes, for example Mail sync, while also reducing the screen's brightness.

It also slows your iOS device down quite a bit, so don't try playing any of those high-performance mobile games with it on. It may be worth it though. According to Wired's complicated tests and mathematics, it should make the battery last about 1.43 times longer. You can enable or disable it manually, but once your iPhone hits 20 percent battery life, you'll get an automatic prompt to enable it.

Finally, there's one more change (also Android-inspired) that makes switching between running apps much easier. It's the back button on the top-left of the screen, which is now smarter and more contextual, enabling you to switch from one open app back to the different, previously open app -- all without hitting the "Home" button. But if you prefer the app switcher, it's been visually improved by stacking the recently-used app panes, rather than having them lay full and flat.

What are your favorite new features of iOS 9? What changes could you live without? Let us know in the comments below!