17. When dividing one number by another, we obtained a decimal fraction, the integer part of which is equal to the divisor, and after the decimal point, the dividend is written. What are these numbers?
17. Let the required numbers be $a$ and $b$, then $a: b=b, a$ or after multiplying by 10 we get $10 a: b=10 b+a$. Since $a$ does not divide evenly by $b$, then the number 10 must divide by $b$, which means $b=2$ or $b=5(b \neq 10$, otherwise we would get $a=100+a$, which is impossible). If $b=5$, then $2 a=50+a$, from which $a=50$, and then $50: 5=10$, which does not satisfy the condition. If $b=2$, then $5 a=20+a$, from which $a=5$, and then we have $5: 2=2.5$. Therefore, $a=5$ and $b=2$.