What Positive Number Doubles When Its Last Digit Becomes Its First Digit?

If the last digit of this positive number becomes the first digit, the resulting number is exactly twice as large. My number is the smallest positive number with this property. What is my number?

You might be able to find some numbers that almost work.

25 would become 52, which is close to 25(2) = 50

102 would become 210, which is close to 102(2) = 204

What is my number? I’ll give you a hint: you are unlikely to solve for the answer by casually guessing it. But a genius might be able to. Legendary mathematician Freeman Dyson apparently heard the problem and instantly replied with the number of digits in the answer.

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