The decimal representation for 1/7s is really cool

I knew it was the same cycle shifted, but it never occurred to me that means the first digit has to be sorted like that. But it's obvious now that has to be so. Very cool!

I remember figuring this out in middle school, then impressing my math teacher when he'd have some number divided by 7 and I blurted out the answer to six decimals! Btw, to remember the sequence, 7 x 2 = 14 x 2 = 28 x 2 (+1) = 57 .... 142857

I was playing around with the collatz problem the other day and the fractions of the decimals would tell me the numbers to hit the max 9232 I think fractions and decimals is telling a lot more information than we know

“When will I use this” For roughly estimating USD to AUD conversions

Used this in a Yr6 Special Skills presentation, claiming I can divide any number between 1 and 100 by 7. If you don't know the pattern it seems like a magic trick.

"And 6/7th" Please don't do it, please don't it, please don't do it.

very cool.... i like also that each two digits is half the value of the second two digits... 14, 28, 57 the last two here are not exact... but close enough to be interesting fun Pi fact... the 359th digit of pi start the three digits '360'... Pi is related to the circle... there are 360 degrees in a circle... "coincidence"? @iamlisakirk @GGxTrades

142857 is a circular number. There are countless funny things about it. 14 + 28 + 57 = 99 142 + 857 = 999 It also cycles when you multiply it (142857 * 2 = 285714, etc 857^2 - 142^2 = 714285

So 1/7 + 6/7 = 7/7, which is 0.999999?

I think what you’re doing with math is beautiful. Thank you for the inspiration.

I don’t understand what he means when he says that you go to “the next digit in increasing order.” Like, those words don’t mean anything.

1->2->4->5->7->8

Thanks for explaining. For me at least, the original wording needed to be fleshed out a little. It sounded to me like it meant something like, go to the next number that is higher than the last. So if the number was 1, the next number that was any higher than1 would be chosen.

@howie_hua it was minimum among higher numbers

@howie_hua I understand that. My point is to give feedback that the way it was described wouldn’t necessarily communicate it to those who aren’t using these concepts regularly.

I saw an amazing astronomy lecture a while ago, and in the first lecture he gave rules of thumb for calculating quick estimates: pi=3 =sqrt 10 =2 x sqrt 2 These would give estimates within an order of magnitude, which is enough to test an idea. Now I'm adding: 1/7 = (sqrt 2)/10

If you take the first three digits of the repeating pattern and add it to the second three digits they always add up to 999 for example 142 + 857 = 999, 285 + 714 = 999

@SimplyAwakeX Something is off bc the decimal for 1/7 plus the decimal for 6/7 should be 1.0 but it’s .999999

In base 7, it is just "0.1"

Due to one simple way in which you can build repeating decimals, i.e., 1/9 = 0.9..., 2/9 = 0.2..., 32/99 = 0.32..., and the fact that 1/7 = 0.142857..., this means that 999999/142857 = 7. This is pretty simple, but I love it.

I wonder what happens for 7/7...

That shirt is amazing!!

That would be so fun for my 6th graders to explore!

Nice, I suppose the only time you would realistically use this in your daily life would be representing the days as a decimal of a week.

"Math is not just truth, but true beauty". Thanks for sharing

Hi Howie. You own a huawei? How was Hawaii?

6/7

Looks like m/7 = Σ(n=1→∞) 7m×0.02^n

then what's 7/7?

I remember working out this repeat in high school math class and being amazed. It's easy to see it yourself, you just use the long division algorithm and keep dividing.

Math is so fun!!!! What a lovely discovery.

You probably won't "use it." Playing with numbers to the point where you find this interesting, especially while young, increases your "numeracy," which is a valuable and increasingly rare trait.

love it!

I didn't know Manny Pacquiao was a math bug.

It's the same with 1/17 😱🤪😱🙈

My father taught me this when I was about 8. Extremely useful thing to know because it helps make estimates quickly, as well as the actual fractions.

why's he kinda...

I have used that on numerous occasions.

Ass hole didn't show us what 7/7 would be.