A rather long number ends with an 8 If this digit ie the 8 is shifted to the front position you obtain a number twice the original number Find this number?

Answer 1

The number is 421052631578947368 multiplied by 2 equals

842105263157894736.

The 8 moves from front to back

Here is one way on how to solve this problem:

Start with the ones digit. So the number with 8 in the ones position is multiplied by 2 to get the second number.so we have:abcdefgihjk8x 2------------8abcdefgihjkwhere each of the letters represents a digit. But we don't know how many digits there are.So start with the ones digit and get 2 * 8 equals 16, so k equals 6Carry the 1 and you get 2 * k + 1 equals j, we found that k equals 6,so j equals 2 * 6 + 1 equals 13 (or 3 carry 1), so j equals 3.Keep going and eventually you get all the numbers, then the sequence starts repeating. I made a spreadsheet to do it all for me.In column A will be the first number (the one to be multiplied by 2). Column B will the multiplication.Each row represents the position in the number, sorow 1 represents the ones place, row 2 the tens place, etc.So the first number has 8 in the ones place, so cell A1 equals 8in cell B1, I put this formula: = A1*2So 8*2 equals 16, but we want the next 'digit' to be six (6) and then carry the one (1) into the next calculation. So here'sthe formula I put into cell A2:= B1-10*(INT(B1/10))so we divide 16 by 10 equals 1.6, then take the integer of thatequals 1, then multiply back by 10 equals 10, then subtract theresult from 16 equals 6, which is the digit we want in thatposition.For cell B2: = A2*2+INT(B1/10)which takes 'B1' which holds the 16, divides by 10 to get1.6, then takes the integer to get 1. This is our 'carry'which is added to the result of 6*2, so we have 6*2+1 equals 13.Then just copy cells A2 and B2 down, and read off the numbers. On row 19, cell A19 has a value of 4, and there will not be a 'carry' digit, so that 4 * 2 equals 8, and thesequence repeats, so you're done.8 166 133 77 144 99 188 177 155 111 33 66 122 55 100 11 22 44 8 <------- right here it will start repeating8 166 133 7 etc.so then the first number is, starting at cell A18,and reading 'up' we get 421052631578947368Multiply it by 2 and get 842105263157894736