> a/2^b. Then the mantissa is a, and the exponent is -b Why not just write a * 2^b. Your a here, if supposed to represent the mantissa, is not an integer. This

> a/2^b. Then the mantissa is a, and the exponent is -b Why not just write a * 2^b. Your a here, if supposed to represent the mantissa, is not an integer. This form doesn’t really clarify the relationship to the concept of a dyadic rational. To write the floating point number as a dyadic rational treating a as an integer you would have something like (2^(53) + a) / 2^(53 - b). But arbitrary dydadic rationals cannot be represented by a single floating point number. If you want arbitrary dyadic rationals you need the sum of a list of floats. * * * I think what you might be getting at is starting by teaching people about fixed-point binary numbers? Or just binary fractions in general, analogous to the usual decimal fractions? That would be clearer to say than anything about “dyadic rationals”. After going through a typical primary school, people have the concept of “terminating decimals”, rather than a concept of “ten-adic rationals”.