Counting to one billion

The idea of counting to a billion recently came up in conversation, which naturally led to Googling “how long does it take to count to one billion?” And that has obviously resulted in what is clearly the nerdiest thing IÂ’ve ever written.

A lot of people seemed to say it would take a billion seconds – attributing one second to each number. IÂ’m no mathematician, but right away I can see thereÂ’s something flawed with that reasoning. After all, it takes a lot longer to say “nine-hundred-ninety-nine-million-nine-hundred-ninety-nine-thousand-nine-hundred-ninety-nine” than it does to say “one”.

For example, I can easily count to ten in 1.3 seconds. However, it takes me 2.4 seconds to say “999,999,999″. It took me 36.1 seconds to count to one hundred, and that required a moderate amount of concentration. It also took me 14.5 seconds to count from 798,457,982 to 798,457,984 – which is only 3 numbers and thus more than 4.8 seconds per number. I was also reading those numbers off a page (which is likely what most non-autistic people would have to do anyway).

Not being mathematically inclined, I couldn’t make up a fancy-looking equation but I managed to work it out in a rather ugly way.

Some results from randomly chosen number groups:
1 – 10: 1.3 seconds (0.13s/number)
1 – 100: 36.1 seconds (0.36s/number)
101 – 110: 7.7 seconds (0.77s/number)
1,430 – 1,440: 18.4 seconds (1.8s/number)

Before even getting to 5-digit numbers it’s taking me almost 2 seconds to count one number – and the majority of numbers when counting to a billion are all well over five digits in length.

It also took me 2 minutes and 37.6 seconds (or 157.6 seconds) to count to two hundred which is 0.788 seconds per number. I really donÂ’t want to count to a thousand, but itÂ’d probably take me around 13 minutes. However, one to one thousand is a minuscule and more or less irrelevant part of the picture. There are only 901 three-digit numbers and 99 two-digit numbers, while there are 9,000 four-digit numbers, 90,000 five-digit numbers, 900,000 six-digit numbers, 9,000,000 seven-digit numbers, 90,000,000 eight-digit numbers, and 900,000,000 nine-digit numbers.

I chose random blocks of ten consecutive numbers to count in each of the “digit categories” and timed how long it took verbally count them out. Then I divided by ten to come up with a “per number” time.

Four-digit numbers: 1.6 x 9,000 = 14,400
Five-digit numbers: 1.98 x 90,000 = 178,200
Six-digit numbers: 2.98 x 900,000 = 2,682,000
Seven-digit numbers: 3.66 x 9,000,000 = 32,940,000
Eight-digit numbers: 4.16 x 90,000,000 = 374,400,000
Nine-digit numbers: 5.24 x 900,000,000 = 4 716,000,000

Therefore the total number of seconds is 5,126,214,600. ThatÂ’s 1,423,948.5 hours or 162.55 years. And that’s added to the 13 minutes counting to a thousand to start things off.

And that’s 162-and-a-half years counting non-stop, without eating, drinking or sleeping… or losing count.

Therefore I think it’s safe to say that no man or woman has ever counted to a billion, and no one ever will. Except perhaps Rain Man.

Tagged as: Fun, random