Converting fractions from one base to another is a fundamental mathematical operation. In this article, we will focus on converting the fraction 5 16 to its decimal equivalent. We will discuss the step-by-step process, explore the concepts involved, and provide real-world examples to enhance your understanding.
The base of a number system refers to the number of unique digits used to represent numbers. In our decimal system, we use 10 digits (0-9), while in the hexadecimal system (base 16), we use 16 digits (0-9 and A-F).
To convert 5 16 to decimal, we need to decompose the fraction into its individual components:
5 / 16 = (5 * 16^-1)
Now, we can convert each component to its decimal equivalent:
16^-1 = 0.0625
Substituting this back into our original equation, we get:
5 / 16 = (5 * 0.0625) = **0.3125**
Therefore, 5 / 16 = 0.3125 in decimal notation.
Example 1:
A computer scientist needs to convert a hexadecimal color code (#5F6E) to its decimal equivalent to set the background color of a website.
Example 2:
An engineer is working with a hexadecimal address (0x5A) in a memory system. They need to convert it to decimal to locate the corresponding memory module.
Example 3:
A programmer is debugging a hexadecimal error code (0x7E) in a software application. Converting it to decimal helps them identify the specific error type.
Converting fractions from one base to another is essential in various fields, including:
Story 1:
A software developer accidentally used a hexadecimal value (#FF00FF) instead of a decimal value (255, 0, 255) in their code. This resulted in an incorrect color display in the application. Lesson: Paying attention to bases and converting values accurately is crucial in programming.
Story 2:
An electrical engineer was diagnosing a problem with a circuit board. The error code displayed in hexadecimal (0x7A) puzzled them. After converting it to decimal (122), they identified the faulty component. Lesson: Hexadecimal conversions help engineers troubleshoot errors efficiently.
Story 3:
A mathematician was studying a number sequence in which each term was expressed in a different base. By converting the terms to decimal, they were able to discover a hidden pattern. Lesson: Understanding base conversions enables mathematicians to explore and solve complex problems.
Converting 5 16 to decimal requires a clear understanding of bases and number systems. By following the step-by-step approach and effective strategies outlined in this article, you can confidently convert fractions between different bases. Mastering these conversions is essential in various fields, from computer science and engineering to mathematics and data analysis.
Table 1: Base Conversion
Base | Digits |
---|---|
Decimal | 0-9 |
Hexadecimal | 0-9, A-F |
Binary | 0, 1 |
Octal | 0-7 |
Table 2: Hexadecimal to Decimal Equivalents
Hexadecimal | Decimal |
---|---|
0 | 0 |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
8 | 8 |
9 | 9 |
A | 10 |
B | 11 |
C | 12 |
D | 13 |
E | 14 |
F | 15 |
Table 3: Fractions to Decimal Equivalents
Fraction | Decimal |
---|---|
1 / 16 | 0.0625 |
1 / 8 | 0.125 |
1 / 4 | 0.25 |
1 / 2 | 0.5 |
1 | 1.0 |
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