Look at some decimal expressions of fractions such as 2,3 25¹ 8 15 20 14¹ 50 12 7 9 16 71 50 54,30 by carrying out long divisions or using your calculator (Careful, calculators can give mis- leading results!), and see which numbers have a terminating decimal expression, while paying attention to the prime factorisation of the denominator. Hint: Take a terminating decimal expression and see what happens when you convert it to a fraction in lowest terms. (Don't include this part in your homework submission.) Now come up with a conjecture for which fractions have a terminating decimal expres- sion. Your conjecture should be of the following form: Let a, bEN with b>1 and with gcd (a, b) = 1. Then a has a terminating decimal expression iff

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