How can I easily double any size number in my head?

I'm a software engineer, and I often double numbers especially when doing binary to decimal conversions. When numbers get large, I have trouble doubling a number in my head without using paper. For example, I can double 128 in my head easily because it's common and I have it memorized, but numbers like 183 get more difficult.

Is there some clever trick I can use to mentally double any number? I'm probably being idealistic, but it would be nice to have 4 digit numbers be just as easy to double as 2 digit numbers.

Solution 1:

I usually look for an easy calculation that is close by the original one.

For example:

$2 \times 183 = 2 \times 180 + 6=366$

or

$ 2\times 1481= 2 \times 1500 - 38 = 2960+2$

Solution 2:

It may help to partition the number into smaller numbers that lead with a number less than 5. The idea being that you can double each of these smaller numbers independently then combine their answers without having to worry about "carrying the one".

Example: $$18397238$$ Partitions into $$\underline{18}\,\underline{397}\,\underline{2}\,\underline{38}.$$ Doubling each one yields $$\underline{36}\,\underline{794}\,\underline{4}\,\underline{76}$$

This is efficient if there are a lot of numbers less than $5$ in your number, but not so much otherwise.

Edit: It should be noted that this technique can work in tandem with many of the other methods mentioned, and can actually make them easier to use. For example, if you first think of the number grouped according to my strategy, then use the left-to-right method outlined in David K's answer on each group, every digit has a carried 1 except the last, so you don't even have to think about what the digit to the right is when you are doubling.