Ten number ending in 9 is essentially the same as those same ten numbers but ending in zero plus ten nines.
$1.19 = $1.10 + 0.09
$1.19 + $1.69 = $1.10 + $1.60 + (2 * 0.09)
Since there were 10 items, each ending in a 9, that’s the same as 9 times 10, or in this case $0.09 * 10. Every time you multiply by 10 you end up with a zero on the end.
In a base 10 system multiplying by 10 basically shifts all the digits over by 1 and adds a zero to the end. Whatever was in the 10s spot goes in the 100s spot. Whatever was in the 100s spot goes in the 1000s spot, and so on.
So, if you buy 10 items with a 9 at the end of their price, you’ll always end up with a zero in the cents spot. If you buy 100 items like that, your total will be in dollars with zero cents.
What’s more impressive here is that so many of the other digits ended up as zero when there was no pattern. Ten items ending in ‘9’ means that you carry over a ‘9’ to the next column, but to get that to be zero means the sum of all the tens (of cents) digits needed to end up in a 1.
1 + 6 + 9 + 4 + 9 + 9 + 6 + 6 + 2 + 9 = 61
And to get to exactly 40, the dollars digits needed to match that 6 plus 1 carried over (1 + 9), so they needed to end in 3 (or to be 33 exactly for the total to be 40):
1 + 1 + 6 + 5 + 3 + 3 + 5 + 5 + 3 + 1 = 33
Ignoring the fact that grocery stores suck and price things ending in 9 all the time, it’s a 1/10 shot to get the cents digit to end up as a zero, a 1/10 shot for the hundreds to end up as zero, and 1/10 for the dollars digit to end up as a zero. OP just used up a lifetime of luck for a 1/1000 occurrence.
Ten number ending in 9 is essentially the same as those same ten numbers but ending in zero plus ten nines.
$1.19 = $1.10 + 0.09
$1.19 + $1.69 = $1.10 + $1.60 + (2 * 0.09)
Since there were 10 items, each ending in a 9, that’s the same as 9 times 10, or in this case $0.09 * 10. Every time you multiply by 10 you end up with a zero on the end.
In a base 10 system multiplying by 10 basically shifts all the digits over by 1 and adds a zero to the end. Whatever was in the 10s spot goes in the 100s spot. Whatever was in the 100s spot goes in the 1000s spot, and so on.
So, if you buy 10 items with a 9 at the end of their price, you’ll always end up with a zero in the cents spot. If you buy 100 items like that, your total will be in dollars with zero cents.
What’s more impressive here is that so many of the other digits ended up as zero when there was no pattern. Ten items ending in ‘9’ means that you carry over a ‘9’ to the next column, but to get that to be zero means the sum of all the tens (of cents) digits needed to end up in a 1.
1 + 6 + 9 + 4 + 9 + 9 + 6 + 6 + 2 + 9 = 61
And to get to exactly 40, the dollars digits needed to match that 6 plus 1 carried over (1 + 9), so they needed to end in 3 (or to be 33 exactly for the total to be 40):
1 + 1 + 6 + 5 + 3 + 3 + 5 + 5 + 3 + 1 = 33
Ignoring the fact that grocery stores suck and price things ending in 9 all the time, it’s a 1/10 shot to get the cents digit to end up as a zero, a 1/10 shot for the hundreds to end up as zero, and 1/10 for the dollars digit to end up as a zero. OP just used up a lifetime of luck for a 1/1000 occurrence.
To OP: GG Cheese!
Dang, thanks for doing that math! That’s super interesting.
Thanks for your more than mildly interesting post.