## Related questions with answers

The tenth digit that you found in the earlier problem is the check digit. It is used to detect and correct errors that may occur when the ZIP code is read, recorded, or transmitted by a computer. In this problem, you will discover how the check digit works.

a. Add up all nine digits in the ZIP code on the reply card, and also add the tenth check digit. Then reduce mod 10.

b. Repeat Part a for the following three additional ZIP codes, with indicated check digits.

i. 47402-9961, with check digit 8

ii. 80323-4506, with check digit 9

iii. 02174-4131, with check digit 7

c. By examining the results in Parts a and b, state a rule for how the check digit works. Compare your rule with that of others and resolve any differences.

Solution

Verifieda.)

Add all the digits in the ZIP code $321429143$:

$\begin{aligned} 3+2+1+4+2+9+1+4+3=29 \end{aligned}$

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