Question

Account numbers sometimes contain a check digit that is the result of a mathematical calculation. The inclusion of the digit in an account number helps ascertain whether the number is a valid one. Write an application named CheckDigit that asks a user to enter a four-digit account number and determines whether it is a valid number. The number is valid if the fourth digit is the remainder when the number represented by the first three digits of the four-digit number is divided by 7. For example, 7770 is valid, because 0 is the remainder when 777 is divided by 7. If the account number is valid, output The account number is valid. If the account number is invalid output Invalid. If the account number is too short or too long output Account number invalid - it must have 4 digits.

Answer 1

A four-digit account number is valid if the fourth digit is the remainder when the number represented by the first three digits is divided by 7.

Step-by-step explanation:

In order to determine if a four-digit account number is valid, you need to follow a specific calculation. The fourth digit of the account number should be the remainder when the number represented by the first three digits is divided by 7. For example, if the account number is 7770, you need to divide 777 by 7, which gives you a remainder of 0.

If the remainder matches the fourth digit, then the account number is valid. If it doesn't match or if the account number has fewer or more than 4 digits, it is considered invalid.

For the CheckDigit application, you can ask the user to input a four-digit account number and then perform the necessary calculations to determine its validity.

Answer 2

The CheckDigit application considers a four-digit account number valid if the fourth digit is the remainder of dividing the first three digits by 7. Account numbers not matching this rule or not having four digits are deemed invalid. The concept of significant figures is important to ensure precision in the result.

Step-by-step explanation:

The CheckDigit application is designed to validate a four-digit account number by using a mathematical check involving a check digit. To determine if an account number is valid, the application asks the user for the number, extracts the first three digits, and divides this number by 7. The remainder from this division should match the fourth digit of the provided account number for it to be considered valid.

For instance, the account number 7770 is valid because when the number 777 is divided by 7, the remainder is 0, which matches the fourth digit. If the fourth digit does not match the remainder, the account number is declared invalid. Additionally, if the entered account number is not exactly four digits long, the application will output that the account number is invalid and must consist of precisely four digits.

It's important to note the relevance of significant figures and rounding errors. When performing mathematical operations, especially division and subtraction, we should match the preciseness of our result with the significand of the original data to avoid overstated precision.