Learn Turkish: Yeni batarya ile menzil yüz kilometre artıyor. - With the new battery, the range increases by a hundred kilometers.

You would simply put ne kadar (how much) right before the verb: Yeni batarya ile menzil ne kadar artıyor? Just like in the statement, you don't need a Turkish equivalent for the English word "by".

Why isn't there a word for "by" before yüz kilometre?

In English we say something increases or decreases "by" a certain amount, but Turkish doesn't use an extra word for this. With verbs of changing quantity like artmak (to increase) and azalmak (to decrease), you just state the bare amount directly before the verb.

I originally learned that battery is pil. Why does this sentence use batarya?

Pil generally refers to standard, interchangeable batteries (like AA or AAA batteries). Batarya refers to larger or integrated rechargeable batteries, like those in laptops, phones, and electric vehicles. Because the sentence mentions menzil (range), it's almost certainly talking about an electric car.

Can I combine batarya ile into a single word?

Yes, you can attach ile (with) as a suffix. Because batarya ends in a vowel, you must add the buffer letter y, making it bataryayla. Both batarya ile and bataryayla are perfectly correct, though the suffix version is more common in spoken Turkish.