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A normal boy becomes a candidate for the God of Math.
He then went to the dormitory for the candidates
and was given room 142857.
The Secret of the Number 142857
However,
no matter how hard he tries, the room won’t open.
"The game for becoming the God of Math has already started.
To open the door, you should unravel the secret of the room number."
What on earth is the secret of this plain number?
At that moment, his old teacher comes to visit him unexpectedly.
Multiply 142857 by the numbers from 1 to 6 in order.
Well, did you find something?
Wow! The digits of 142857 always appear in the same set of products
but are different in terms of the order of the numbers.
If you multiply 142857 by 7...
How amazing!
It becomes a number consisting of only of the digit 9.
Right. Now let me show you something more amazing.
Split it into two-digit and three-digit numbers and then add them.
Oh my God!
It’s too early to be surprised.
Now square the number 142857, divide it into two parts, and then add them.
Oh my goodness! It gets back to the original number.
Right! So where does this magical number come from?
Turn 1/7 as a decimal.
Oh! The number 142857 is shown repeatedly!
Well, we’re almost there. Did you notice the answer?
In the fractions whose denominators are 7 and numerators is the numbers from 1 to 6,
142857 is shown repeatedly but changes position.
What do you call a decimal like this that has repeating certain digits after the point?
A repeating decimal.
In contrast,
what do you call a decimal like this that has a finite value after the point?
A terminating decimal.
So all fractions come down to terminating decimals, such as 1/2 and 1/4,
or repeating decimals, such as 1/7 and 1/3.
Well now, if you shout out the secret of this room number, the door will open.
The secret of the number 142857 is...
a repeating decimal.
The door finally opens.
However, even though he tries so many times, the light won’t turn on.
"The game for becoming the God of Math is still in progress.
Because of this, tell me the other secret of this repeating number."