# Math Help - 8x

1. ## 8x

If $x=0.1234567891011121314151617181...303132333...$

find $8x$

2. $x=0.123456789101112131415161718192021...$

This number is called Champernowne Constant.

It's given by

Since it's a transcendental number, I can't see a way to multiply it by 8..

$8x = 0.987654312808897051321293745536169778594021018263 4425058667...$

3. Break the number x into chunks, where each chuck starts with a 0 and ends just before the next 0 (and must include some nonzero digits). 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.