What 5-digit number has the following features: If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number?

Let the 5 digit number be represented by abcde.
Then the 6 digit number, 1abcde x 3 = abcde1 (another 6 digit number)
Now let Y = abcde.00
Then (100000 + Y) x 3 = (Y x 10) + 1
300000 + 3Y = 10Y + 1
7Y = 299999
Y = 299999 ÷ 7 = 42857

Check : 3 x 142857 = 428571