The use of 'a/an' when something is mentioned for the first time

A/an is used before a countable noun mentioned for the first time: the

speaker assumes the listener does not know what is referred to: / looked up and saw a plane (Mentioned for the first time - you don't know which plane I mean.) The plane flew low over the trees (You now know exactly which plane I mean and the plane is, in that sense, identified.) [> 3.20.1]

This rule governing the choice between definite and indefinite article is

common in European languages.

3.11 The difference between 'a/an' and 'one'

One and a/an cannot normally be used interchangeably. We use one when we are counting (one apple, as opposed to two or three):

It was one coffee we ordered, not two But we could not use one to mean 'any one' (not specified):

A knife is no good You need a screwdriver to do the job properly

One is often used with day, morning, etc. in story-telling:

One day, many years later, I found out what had really happened
A/an and one can be used interchangeably when we refer to:
Whole numbers: a (or one) hundred, thousand, million [> App 47]
Fractions: a (or one) quarter, third, half, etc.

Money: a (or one) pound/dollar, etc. We say 'One pound 50

Weight/measure: a (or one) pound/kilo, foot/metre, etc.

A/an and one are interchangeable in some expressions (with a/one blow), but not in others (a few). For one as a pronoun [> 4.9-11].

The use of 'a/an' with reference to measurement

A/an is used when we refer to one unit of measurement in terms of
another. If we want to emphasize 'each', we use per instead of a/an:
Price in relation to weight: 80p a/per kilo

Distance in relation to speed: 40 km an/per hour

Distance/fuel consumption: 30 miles a/per gallon

Frequency/time: twice a/per day

3.13 The use of 'a/an' after 'what' and 'such'

A/an is used with countable nouns after What in exclamations:

What a surprise! What an interesting story¹ A/an is used after such when we wish to emphasize degree [> 7.51.1]:

That child is such a pest¹ My boss is such an idiot! What a lot ' (Not "How much/many...!*) is used for exclamations:

What a lot of flowers! What a lot of trouble'

The use of 'a/an' with pairs of nouns

Many nouns are 'paired', that is they are considered to accompany each other naturally, and a/an is used before the first noun of a pair: a cup and saucer, a hat and coat, a knife and fork-It s cold outside Take a hat and coat with you

^s The definite article 'the'

If two words are used which are not considered to be a 'natural pair', the indefinite article must be used before each noun: When you go on holiday, take a raincoat and a camera