MATHS 2 Assignment: Ratio, Checksums, Modular Arithmetic, and UPCs

This document presents a solved MATHS 2 assignment, demonstrating the conversion of decimals to ratios, including examples like 0.96, 5.92, 1.47381, -387.4, and -0.00006. It then delves into checksum calculations, verifying UPC codes using a specific algorithm and identifying errors. The assignment also explores modular arithmetic, specifically calculating 5^628 mod 7 using the properties of exponents and modular congruence. Additionally, the assignment includes a coded message, requiring decryption. This solution is provided by a student and is available on Desklib, a platform designed to provide students with AI-based study tools, including past papers and solved assignments.

Running head: MATHS
MATHS
Name of the Student:
Name of the University:
Author Note

1
MATHS
Decoding decimals
0.96 = 96/100 = 24/25
Therefore, the ratio is 24: 25
5.92 = 592/100 = 148/25
Therefore, the ratio is 148: 25
1.47381 = 147381/100000
Therefore, the ratio is 147381: 100000
-387.4 = -3874/10 = -1937/5
Therefore, the ratio is -1937: 5
-0.00006 = - 6 /100000 = -3/50000
Therefore, the ratio is -3: 50000
Applesauce
0 28500 11070 x
It has been assumed that the missing digit be x.
Therefore, the addition of the odd numbers = 0 + 8 + 0 + 1 + 0 + 0 = 9
Multiplying the result by 3 we get, 27.
Addition of the even terms:
2 + 5 + 0 + 1 + 7 = 15

2
MATHS
Addition of 2 results:
27 + 15 = 42
42 mod 10 = 2
Therefore, the final number is 10 – 2 = 8.
Therefore, x = 8.
Progresso
0 05055 00505 3
Therefore, the addition of the odd numbers = 0 + 5 + 5 + 0 + 5 + 5 = 20
Multiplying the result by 3 we get, 60.
Addition of the even terms:
0 + 0 + 5 + 0 + 0 = 5
Addition of 2 results:
60 + 5 = 65
65 mod 10 = 5
Therefore, the final number is 10 – 5 = 5.
Checksum for 0 05055 00505 3: 5
The checksum does not match.

3
MATHS
0 52010 00121 2
Therefore, the addition of the odd numbers = 0 + 2 + 1 + 0 + 1 + 1 = 5
Multiplying the result by 3 we get, 15.
Addition of the even terms:
5 + 0 + 0 + 0 + 2 = 7
Addition of 2 results:
15 + 7 = 22
22 mod 10 = 2
Therefore, the final number is 10 – 2 = 8.
Checksum for 0 52010 00121 2: 8
The checksum does not match.
0 41196 01012 1
Therefore, the addition of the odd numbers = 0 + 1 + 9 + 0 + 0 + 2 = 12
Multiplying the result by 3 we get, 36.
Addition of the even terms:
4 + 1 + 6 + 1 + 1 = 13
Addition of 2 results:

4
MATHS
13 + 36 = 49
49 mod 10 = 9
Therefore, the final number is 10 – 9 = 1.
Checksum for 0 41196 01021 1: 1
The checksum matches
Therefore, the correct UPC is 0 41196 01021 1.
Big and power format
Now, 5^4 (mod 7) = 2
5^628 (mod 7) = x
Or, (5^4) ^157 (mod 7) = x
Or, x = 2
Therefore, 5^628 = 2 (mod 7).
Secret Admirer
PBDU TFQ DKBFU