Jim uses his calculator to see if a number n having eight or fewer digits is divisble by a number d. He finds that n / d has a display of 32. Does d|n? Why?
b. If n / d gives a display of 16.8, does d|n? Why?
To determine whether a number n is divisible by a number d using a calculator, we need to check if the result displayed is a whole number, or if it has any decimal places.
In the first case, Jim finds that n / d has a display of 32. So, in this case, if n/d is equal to 32 and the number n has eight or fewer digits, it means that the calculator displayed a whole number as the result. This implies that d divides n evenly without any remainder, so we can say that d|n.
In the second case, Jim finds that n / d has a display of 16.8. Here, the displayed result has a decimal portion of ".8," indicating that n/d is not a whole number. In this scenario, d does not divide n evenly, and thus, we cannot say that d|n.
To summarize,
b. If n / d gives a display of 16.8, d does not divide n evenly, so we cannot say that d|n.