Decimal equivalent

Definition

The decimal equivalent is a representation of a number from a different base system in base ten, which is the standard numbering system used in everyday arithmetic. Understanding decimal equivalents allows for easier computation and comparison between numbers expressed in various bases, such as binary or hexadecimal. This concept also plays a significant role in converting percentages into decimal form, facilitating calculations involving ratios and proportions.

5 Must Know Facts For Your Next Test

1. To find the decimal equivalent of a number in another base, multiply each digit by the base raised to the power of its position and sum the results.
2. For example, the binary number 1011 can be converted to decimal by calculating: 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11.
3. When dealing with percentages, converting them to decimal form involves dividing the percentage by 100, making calculations simpler.
4. Decimal equivalents are crucial in fields like computer science and finance where different base systems and percentages are frequently used.
5. Understanding how to convert numbers to their decimal equivalents can enhance problem-solving skills and accuracy in various mathematical applications.

Review Questions

• How do you convert a binary number like 1101 into its decimal equivalent? Explain the process.
  • To convert the binary number 1101 into its decimal equivalent, start by identifying the value of each digit based on its position. The leftmost digit represents $2^3$, the next $2^2$, then $2^1$, and finally $2^0$. So for 1101, you calculate: 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13. Thus, the decimal equivalent of the binary number 1101 is 13.
• What is the significance of understanding decimal equivalents when working with percentages in mathematical calculations?
  • Understanding decimal equivalents when working with percentages is crucial because it simplifies calculations. When percentages are expressed in decimal form, operations like addition, subtraction, multiplication, and division become straightforward. For instance, converting a percentage like 25% into its decimal equivalent (0.25) allows for easier calculations in real-world scenarios such as discounts or interest rates. This understanding ensures accuracy and efficiency in problem-solving.
• Analyze how knowledge of decimal equivalents impacts practical applications in technology and finance.
  • Knowledge of decimal equivalents has a significant impact on practical applications in technology and finance. In technology, especially in programming and data analysis, converting numbers between different base systems is essential for efficient processing and representation of data. In finance, understanding decimal equivalents aids in calculating interest rates, conversions between currencies, and interpreting financial statements accurately. This proficiency ultimately leads to better decision-making and enhanced analytical skills across various fields.

Related terms

Base System: A base system is a method of counting and representing numbers using a specific number of digits, such as binary (base 2), decimal (base 10), and hexadecimal (base 16).

Conversion: Conversion is the process of changing a number from one base system to another, such as converting binary numbers to decimal equivalents.

Percentage: A percentage is a way to express a number as a fraction of 100, often used to compare relative sizes or amounts in different contexts.