Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

Find 8x

If

find  8x

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Find 8x

If x was equal to

, then 8x would be 987654321. (or 80/81)

However, it's actually a bit less than that, because the tenth decimal place is only 1 instead of 10, etc.
I'll try some more to find an exact answer, but it looks like it'll be tricky.

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Why did the vector cross the road?
It wanted to be normal.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Find 8x

Does it end at ...979899, or is there some new pattern after that?

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Wrap it in bacon

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Find 8x

Break the number x into chunks, where each chuck starts with a 0 and ends just before the next 0 (and includes at least one nonzero digit). Multiply each chunk by 8, and then add the chunks up.

For example, the first chunk is 0.1234567891. Multiply that by 8: 0.9876543128.
The second chunk is 01112131415161718192. Multiply that by 8: 08897051321293745536.
Hence the first 31 digits (30 decimal places) of 8x is: 0.987654312808897051321293745536.

Now continue with the third chunk 022122232425262728293, fourth chunk 03132333435363738394, etc.