You have two key elements in obtaining your single, check digit:

1] A key string of numbers, in your case 5432
2] A proper number to use to find the modulus of the product. This is just a way to say the result when given a number we subtract it from the next highest multiple of something, in your case 11. (As you learn more mathematics, you will see this is not the only way to define "modulus"

Now, we take any four-digit string and take the first digit time the first in our key (here five) and sum that product in order through to the fourth number that we want to get a check digit for times the fourth digit in the key (here, two).

Here are your encodings for (a) - Check all this work, to better understand it!

So, for 4388: 4*5 + 3*4 + 8*3 + 8*2 = 30 + 12 + 24 + 16 = ...

Solution Summary

Step-by-step instructions on calculating and verifying check digits using Modulus 11 including a special case.

Given a large number we sometimes need to extract individual digits or sequences of digits from it. For example, given a four-digit year (2010) we may need to extract just the two-digit year or the century. The mathematical operators modulus (Java: %) and division (Java: integer division /) help us with this. Using the operators

1) The definition of length, weight, and modulus of a check digit scheme.
2) Choose one of the schemes discussed in the worksheets and describe it in terms of length weight and modulus. Then illustrate the check digit computation on an ID number valid for that scheme (for example on a book or some product you have handy).

A linear isotropic material has the shear modulus of elasticity G of 11.5*10^6 psi and the Poisson's constant v of 0.3. How do I determine the Young's modulus of elasticity E?

A: Show that the positive integers less than 11, except 1 and 10, can be split into pairs of integers such that each pair consists of integers that are inverses of each
other modulo 11.
Use part (a) to show that 10! is congruent to -1 (mod 11).

A steel wire of length 2.06 m with circular cross section must stretch no more than 0.290 cm when a tensile force of 350 N is applied to each end of the wire.
1. What minimum diameter d_min is required for the wire? Express your answer in millimeters. Take Young's modulus for steel to be Y = 2à?1011 Pa.

A spherical buoy is tied to the sea bed by a steel wire so that exactly half the buoy is above the water surface. If the diameter of the buoy is 1.3m and the mass of the buoy is 20kg:
a) determine the tension in the wire
b) if this tension produces an extension in the steel wire of 4.0mm, calculate the length of the wire.

Let f be analytic in the disk B(0;R) and for 0 =< r < R define
A(r) = max { Re f(z) : |z| = r}. Show that unless f is a constant, A(r) is a strictly increasing function of r.
Please justify every step and claim and show how you used all what is given. Also refer to theorems or lemmas used in the proof. The section where I

Twenty-five samples of steel beam were chosen and tested for Young's Modulus. Eight had a modulus of E = 30 x 10^6 psi. Two had a modulus of E = 29 x 10^6 psi. Fifteen had a modulus of E = 30. x 1-^6 psi.
Estimate the following probabilities:
i) P {E > 29.5 x 10^6 psi}
ii) P {E > 30 x 10^6 psi}
iii) P{E > 28 x 10^6 psi}