Hoping is the present participle of hope. hopping is the present participle of hop. Hoping has only one p while hopping has two. What difference does it make? Why is hoping not hopping?
Edit: I changed mop to hop because of a comment by Kat.
Kat: Why would you compare hope to mop instead of hope to hop (in which case I think your answer will become obvious)?
The p does not get doubled in 'hope' because it's followed by the silent/ magic e. It's called magic e because it's silent itself, but it often changes the pronunciation of the preceding syllable. It turns a vowel to a diphthong or a long vowel. The only common exceptions are words that end in ‹ve› (e.g. love, have).
Examples:
See, the e changes the pronunciation.
The final consonant does not often get doubled when there's a silent e at the end of a word.
'Hope' ends in a silent e, so the p doesn't get doubled.
When a word ends with a consonant, it often (not always) gets doubled. In your examples, 'mop' ends with a consonant, so it gets doubled in present and past participles (regular verbs).
Consonants (often) get doubled in CVC combinations (CVC are the final three elements of a word), where the vowels are represented with a single grapheme, not digraphs.
The last C in CVC is the final consonant.
Examples:
W and Y do not often get doubled when they come at the end.
Examples:
Consonants in CVVC or CVCC combinations (digraphs) do not (often) get doubled.
Examples:
Consonant before magic e does not often get doubled.
Examples:
Consonant after a diphthong does not get doubled. (Almost all the words that have 'diphthong + consonant' often have magic/silent e after the consonant. In fact, the diphthong is a result of adding 'magic e').
Diphthongs are not long vowels. In a 'long vowel', the shape of your mouth does not change while in a 'diphthong', the shape of your mouth changes because a diphthong is the combination of two different vowel sounds.
Examples:
'Hope' has magic e at the end and has a diphthong before p so the p does not get doubled.
In most cases (multisyllabic words, I believe), it depends on stress and does not follow CVC method. When the stress is on the last syllable, the consonant gets doubled.
Examples:
Elicit /ɪˈlɪsɪt/ -> elicited — the T does not get doubled because the last syllable is unstressed.
Interpret /ɪnˈtəːprɪt/ -> interpreted — the T does not get doubled because it's a part of unstressed syllable.
Admit /ədˈmɪt/ -> admitted — the T gets doubled because the last syllable is stressed.
Most words are CVC, though they don't follow the CVC method (e.g. elicit, interpret etc).
(For the letter L, head over to this answer).
Because of the letter e at the end of the word hope.
There is no e at the end of mop. There is the word mope which in its present participle form is spelled moping - note the single p.
Similarly, there's the verb hop (no "e" at the end) which in its present participle form is spelled hopping - not the double p.
While @DecapitatedSoul's answer may be linguistically correct, my answer is much more similar to how @CowperKettle's describes things. It's based on how I learned English and phonics in a English language elementary school in Canada in the 1960s.
In general, English vowels come in two flavours (note the non-American spelling). Those are: short and long. For example, mope has a Long O while hop has a Short O.
So you end up with
| Vowel | Short Examples | Long Examples |
-------------------------------------------------------
| A | apple, hat, cap | cape, hate, grape |
| E | end, den, hell | free, eat, he |
| I | hit, bill, dip | kite, pile, dike |
| O | mop, pot, bob, hop | mope, hope, lone, pole |
| U | hum, tub, cub, run | cure, rule, cube |
Note in the examples I've given, the rule that @CowperKettle mentions mostly holds (except for Long-E, which is special it seems (something I'd never noticed before)). So, if you were to take some of the verbs and form the "-ing" version, you'd end up with
| Vowel | Short Examples | Long Examples |
-------------------------------------------------------
| A | capping, batting | hating, mating |
| E | begging, betting | -doesn't really work- |
| I | hitting, dipping | kiting, piling |
| O | hopping, bobbing | moping, poling |
| U | humming, running | curing, ruling |
English, being English, that's the rule but there are tons of exceptions. However, learning this rule is a great way to get going. It's something that got me through spelling and grammar as I learned English in elementary school.
It's one of those useful language rules (like learning how to conjugate "-er" verbs in French) that gets you 70% or 80% of the way.
Each English vowel letter has two main sounds, one of which is called the "short" vowel sound and the other of which is called the "long" vowel sound. The short vowel sounds are the sounds in the words "bat", "bet", "bit", "bot", and "but" (in IPA /æ, ɛ, ɪ, ɑ or ɒ, ʌ/); the long vowel sounds are the same as the name of the letter (in IPA /eɪ, i, aɪ, oʊ, ju/, although for the letter "u", /u/, the sound in "boot", sometimes acts as a second long vowel sound). (The table in Flydog57's answer has more examples.)
(This doesn't really have much to do with the notions of "long" and "short" in linguistics and doesn't necessarily correspond to what vowels are called "long" or "short" in other languages; just think of them as two arbitrary sounds that happen to be called "long" and "short". Also, each vowel letter has many other sounds as well; English spelling is messy and has lots of exceptions for everything.)
A general rule in English spelling is the vowel-consonant-vowel rule: if you have a vowel letter followed by a single consonant letter and then another vowel letter, the first vowel makes its long sound; in other cases a vowel generally makes its short sound. (This rule only applies in stressed syllables, and doesn't apply when two vowel letters in a row make a single sound; it also has lots of exceptions, like any other English spelling rule.) "Mop" and "hope" are two examples of words that follow this rule: The "o" in "hope" is followed by a consonant letter ("p") and then another vowel letter ("e", which is silent; the second vowel is frequently a silent "e"), and the "o" makes the "long o" sound. The "o" in "mop" is followed only by a consonant letter ("p") but there's no vowel after it, and the "o" makes the "short o" sound.
A problem occurs, though, if you add a suffix starting with a vowel. Usually when you add a suffix like "ing", "ed", "es", or "er", the pronunciation of the word before the suffix stays the same, so "mop" + "ing" is pronounced with a "short o". However, if you wrote it like "moping", then the vowel-consonant-vowel rule would suggest it would be pronounced with a "long o" (like in "hope" or "mope"). In order to keep the pronunciation the same in cases like this, the final consonant is written twice, like "mopping". That way, the "o" is followed by two consonants, and the vowel-consonant-vowel rule doesn't apply.
Separately, there's a rule that when a word ends in a silent "e" and a suffix starting with a vowel is added, the "e" is usually dropped. That means that "hope" + "ing" is spelled "hoping" (and the vowel-consonant-vowel rule still works there, since the "e" is replaced by another vowel).
Again, these are just general rules, and there are lots of exceptions.
Consider the last three letters and apply the CVC rule.
H ope: VCV
Mop: CVC
Hoping: The e gives way to i then ng = Continous
Mop: Double the last C Mopp ing = Mopping
S wim Swim ing = Swimming
prog ram Programm ing = Programming
If a word has 'e" at the end, the final 'e' is dropped and then '-ing' is added to it :
Hope + ing = hoping.
If the last three letters of a word are CVC (Consonant, Vowel, Consonant), the last consonant is doubled when '-ing' is added to it.
Hop + ing = hopping
