- #1

- 92

- 0

What makes the numbers 142[999]857 special?

1/7 = 0.14285714285714..

1/7 = 0.14285714285714..

Last edited:

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter AntonVrba
- Start date

- #1

- 92

- 0

What makes the numbers 142[999]857 special?

1/7 = 0.14285714285714..

1/7 = 0.14285714285714..

Last edited:

- #2

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,025

- 134

- #3

- 92

- 0

142+857=999 is not part of the intended solution

- #4

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,025

- 134

But the rest is?

- #5

- 222

- 0

AntonVrba said:What makes the numbers 142[999]857 special?

1/7 = 0.14285714285714..

:uhh: It only repeats as long as numbers exist??? :surprised

:uhh: Individually they are all less than 10??? :surprised

:uhh: It is a repeating sequence??? :surprised

:uhh: 1+4-2+8-5+7 = 13 and 1-4+2-8+5-7 = -11 with 13-11 = 2 which is "14"/7 and "28"/7 = 4 which is twice 2 and "57" doesn't matter at all because it already has a "7" in it.

It is one of the only short sequence repeating numbers???

- #6

- 92

- 0

Rahmuss said::uhh: 1+4-2+8-5+7 = 13 and 1-4+2-8+5-7 = -11 with 13-11 = 2 which is "14"/7 and "28"/7 = 4 which is twice 2 and "57" doesn't matter at all because it already has a "7" in it.

It is one of the only short sequence repeating numbers???

nice try but none of these or others above

but I like the bit about repeating but what repeats?

- #7

James R

Science Advisor

Homework Helper

Gold Member

- 601

- 15

For example:

1/17 = 0.0588235294117647 0588235294117647 0588235294117647 ...

2/17 = 0.1176470588235294 1176470588235294 1176470588235294 ...

3/17 = 0.1764705882352941 1764705882352941 1764705882352941 ...

Notice the cyclic nature of the decimal expansion.

- #8

- 222

- 0

AntonVrba said:nice try but none of these or others above

but I like the bit about repeating but what repeats?

Well... the "142857" repeats; but that isn't really too special. I'm really either not sure what you're asking, or I'm stumped.

- #9

- 92

- 0

2 x 142[999]857 = 285[999]714

3 x 142[999]857 = 428[999]571

upto

6 x 142[999]857= 857[999]124

the product 2x, 3x, 4x, 5x, 6x of 142[999]857 is always a combination of the same numbers, irrespective of how many times you repeat the nine in the middle

- #10

- 222

- 0

Share: