She spent some time in Asprey’s considering the latest slimline
watches, a gold statue of a tiger with jade eyes and a Faberge egg.
She regretted that her close friend, Tina, was not with her, she
needed her advice badly. From there she walked to a next/nearby shop
which despite a determined salesman who showed her almost everything
the shop had to ...
This is an error. The error seems to be quite common, perhaps as people write "an important" then edit to change "important" to "significant", but forget to change the article. But this is speculation. Nevertheless, it is an error. You shouldn't say (or write) "an significant".
The word "an" is based entirely on the vowel sound of the following word, ...
In this case, the article is optional.
The response is idiomatic both with and without the a. The choice might depend on exactly what's in the respondent's mind when s/he answers.
If the respondent imagines choosing a number from the numbers presented, the answer is likely to be a nine. Similarly a contestant in a TV quiz might choose the (number) nine ...
It's very common to use the article "the" with the phrase "all the ___".
"Pick up all the books."
"All the stores are closed."
This implies a finite concrete list of objects.
Next, what if the article is absent?
"All swans are white."
"All businesses must register with the department."
It's more abstract, not referring to a specific concrete list but ...
"Of importance" is the idiomatic usage, so also "of paramount importance" is the correct usage.
We think of importance as an uncountable noun, so there are not different "importances." As such, there isn't "an importance," either.
Similar usages of of are of note, of interest and of distinction.
No, you should not. "Progress" as you are using it here is uncountable, so you don't use the article. (It may be helpful to think of it this way: if there aren't different "progresses," then it's uncountable and you don't use the article.)
The X means you expect the listener/reader to know which X is meant (it has nothing to do with anything else other than the understanding between speaker/writer and listener/reader).
Talking about the next X typically doesn't work if you don't know which X that is. Otherwise how would you know it's next?
Next can't be used to talk about things that are ...
There's two types of articles - definite (the) and indefinite (a/an). There's also not using an article, sometimes called the zero article.
What does it mean for X definite or indefinite? Definite in this case simply means:
"which X" matters,
the speaker/writer expects the listener/reader to know which X if asked.
"which X" does not ...
We basically never use the with a proper name. For "the Tower" in your text, "the" is part of the name: The Tower of London.
The only exception I can think of is when we use it with a defining phrase. to pick out one of several holders of the name: The John Smith I went to school with; The Brian Cox who is an actor.
The labeling on the Cambridge dictionary website is slightly confusing. Looking at the definition for worsening, we see it is labeled "U or S".
"U" means "Uncountable or singular noun: a noun that has no plural." I think it's saying that if a noun is uncountable, it must be singular. This is true. There is no such thing as a plural uncountable.
Ok, first of all, there's two different questions here. One is what you can say, and the other is what's the best way to say it.
The answer to what you actually can and can't say is different for several of the different items in your examples, and the reason for this is that some of the things you're referring to are countable nouns and some of them are ...