Question: Could I say: 

* a thousand ten (1010),
* a thousand a hundred eleven(1111)

or in these cases I must use **one thousand** instead of **a thousand**? Would using "a" be grammatically incorrect?

Answer: 
Br Eng would be 

> 
> One thousand and ten  
> 
>  One thousand, one hundred and eleven
> 
> 
> 

US Eng seems to miss out the 'and' a lot of the time, but I've never figured the exact pattern, or if it's dialectical, but I've heard such as

> 
> One thousand ten  
> 
>  One thousand, one hundred eleven
> 
> 
> 

but I wouldn't use my guess at how the US does it, I'm a Brit ;)

Neither, though, would use 'a' in that situation, they'd use 'one'.

*From comments:*  

If we are using "whole" numbers, such as 100, 1,000, 1,000,000 etc, then 'a' could be used. A thousand or a million is perfectly acceptable. It just tends not to be used when the number is more 'complex'.
> 
> **Could I say:**  
> 
>  - a thousand ten (1010)  
> 
>  - a thousand a hundred eleven(1111)
> 
> 
> or in these cases I must use one thousand instead of a thousand?
> 
> 
> 

There are a couple of different issues here:

1. Your question is about the difference between saying **a** hundred/thousand or **one** thousand/thousand
2. But you appear to have missed out an "*and*" in your examples too, so we need to address that as well.

Firstly, as a general rule, you can use "a" instead of "one" when referring to hundreds, thousands, millions etc, **only if** there are no other units *greater than tens* that require counting.

> 
> **Examples**  
> 
>  199 = One hundred and ninety nine  
> 
> **or** A hundred and ninety nine  
> 
>  (both of these are acceptable) 
> 
> 
> 1099 = One thousand and ninety nine  
> 
> **or** A thousand and ninety nine  
> 
>  (both of these are acceptable) 
> 
> 
> 1199 = One thousand, one hundred and ninety nine - **correct**  
> 
> **but** A thousand, one hundred and ninety nine - **incorrect**
> 
> 
> 

In that last example it is incorrect for the reason I detailed above - there were *hundreds* to count (one) and so you must also count the thousands (one).

---

Secondly, your example...

> 
> 1010 = a thousand ten - **incorrect**
> 
> 
> 

...is incorrect, **not** because of the "a", but because you are missing an "and". It should be:

> 
> 1010 = a thousand **and** ten
> 
> 
> 

So I'll address that:

**Tens**  

Unlike some other languages, in English there is **no** use of "and" in numbers under 100.

> 
> **Examples**  
> 
>  20 = twenty  
> 
>  21 = twenty one  
> 
>  90 = ninety  
> 
>  99 = ninety nine
> 
> 
> 

**Hundreds**  

Once you reach the hundreds, "and" goes in between the hundreds and the tens.

> 
> **Examples**  
> 
>  100 = one hundred  
> 
>  110 = one hundred and ten  
> 
>  199 = one hundred and ninety nine
> 
> 
> 

**Thousands and higher**  

Once you reach the thousands, the rules above still apply.

You *can* say:

> 
> A thousand  
> 
> **OR**  
> 
>  One thousand
> 
> 
> 

You can also say:

> 
> **A** thousand and ninety nine
> 
> 
> 

But if you have hundreds to count (or thousands, if you've reached a million) then you must number them:

> 
> One thousand, one hundred.
> 
> 
> 

If you have any tens, the "and" goes *before* the tens, *even if there are no hundreds*, like this:

> 
> 1,000,099 = A million and ninety nine  
> 
>  1,100,099 = One million, one hundred thousand and ninety nine
> 
> 
>