 # Decimal

## Definition of Decimal

Decimal is a numerical system based on the number 10, often used for arithmetic operations and calculations. It is also known as the base-10 system, which consists of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In this system, each position in a number represents a power of 10, with the place values increasing from right to left.

### Phonetic

The phonetic spelling of the keyword “Decimal” is: /ˈdɛsɪməl/

## Key Takeaways

1. Decimal is a base-10 number system, meaning it uses 10 unique digits (0-9) to represent numbers.
2. Decimal numbers are widely used in everyday life as well as in various mathematical and scientific calculations.
3. In decimal fractional numbers, each digit’s position signifies the power of 10 it is multiplied by, with whole number positions being positive powers of 10 and decimal places being negative powers of 10.

## Importance of Decimal

The term “decimal” is important in technology because it represents a base-10 numbering system, which is the most widely used and comprehensible system for representing numerical values in everyday life and various applications.

Within technology and computing, the decimal system provides a familiar and convenient way to express data, enabling effective communication and interpretation of information by both humans and machines.

Furthermore, it serves as a fundamental concept in computer programming, data storage, and data processing, as computers internally convert decimal values to other numbering systems, such as binary or hexadecimal, to perform operations more efficiently.

In essence, the concept of decimal is a cornerstone in technology, acting as a bridge between human understanding and computational processes.

## Explanation

Decimal, commonly used in our daily lives, primarily refers to the base-10 numeral system, also known as the decimal or denary system. The purpose of this system is to simplify and unify representations of numbers, allowing for more accessible calculations and mathematical operations. The decimal system introduced an efficient and universal structure for representing numeric values, as it relies on ten distinct symbols – 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 – to denote any value.

Decimal numbers are composed of these digits, strategically positioned according to their place values, which are powers of ten. The familiarity with and ubiquity of the decimal system make it an essential component of modern mathematics, commerce, and various technological fields. The importance of decimals goes beyond simplifying calculations with whole numbers.

Decimals are also widely used to represent fractions and rational numbers accurately. Each decimal place to the right of the decimal point represents a fraction that is a power of ten, such as 1/10, 1/100, and so on. Decimals facilitate precise measurement in various applications, including science, engineering, finance, and everyday problem-solving.

By being able to express a value with a specific degree of precision and in a standardized manner, decimals greatly enhance our ability to comprehend, compare, and manipulate numbers. In various technological settings, the decimal system remains instrumental in coding, programming, and data analysis, where accurate representation and interpretation of numbers are crucial.

## Examples of Decimal

The decimal system, also known as the base-10 numbering system, is widely used in various aspects of everyday life and technology. Here are three real-world examples of where the decimal system is applied:Currency: In most countries, the currency system is based on decimals. For instance, one US dollar is equal to 100 cents, and the decimal point separates the dollars and cents values (e.g., \$

25). This allows for easy calculation and understanding when dealing with money transactions such as making purchases, paying bills, or managing finances.Measurement Units: The International System of Units (SI) utilizes the decimal system for measuring various quantities, such as length, mass, and time. Prefixes are used to indicate the scale, with each step being a multiple of

For example, 1 kilometer is equal to 1000 meters, and 1 millimeter is equal to001 meters. This approach simplifies calculations and conversions between different units.

Digital Electronics and Computing: While most computers and digital systems operate internally on binary (base-2) numbers, they often represent and accept inputs in the decimal format for better human-readability. For example, when entering numbers into a calculator or spreadsheet, we typically use decimal numbers. The device then converts the decimal input into binary for internal processing before converting the result back to a decimal format for human-readable output.

## Decimal FAQ

### What is a decimal?

A decimal is a number system based on the concept of tenths. It uses base 10 and consists of the digits 0-9. Decimal numbers can represent whole numbers as well as fractions.

### How are decimals different from fractions?

Decimals and fractions both represent parts of a whole, but they do so in different ways. Fractions use a numerator and a denominator to represent the part and the whole (e.g., 3/4), while decimals use a decimal point and digits to the right of the point to represent the fractional part (e.g., 0.75).

### Why are decimals important?

Decimals are important because they provide an easy and convenient way to represent, compare, and perform calculations on numbers including fractions. They are widely used in mathematics, finance, measurement, and many other areas.

### How do you convert a fraction to a decimal?

To convert a fraction to a decimal, simply divide the numerator by the denominator. For example, to convert 3/4 into a decimal, divide 3 by 4, which equals 0.75.

### How do you add decimals?

To add decimals, first line up the decimal points and write the numbers one on top of the other. Then, add the numbers just as you would with whole numbers, making sure to bring the decimal point straight down into the answer. If necessary, add zeros as placeholders to make the decimal places align properly.

### How do you subtract decimals?

To subtract decimals, follow the same process as adding, but instead of adding the numbers, perform subtraction. Line up the decimal points, write the numbers one on top of the other, and subtract as you would with whole numbers, making sure to bring the decimal point straight down into the answer.

### How do you multiply decimals?

To multiply decimals, first multiply the numbers as though they are whole numbers. Then, count the number of decimal places in both numbers, and add the counts together. Finally, starting from the right side of the product, insert the decimal point the same number of places from the total count.

### How do you divide decimals?

To divide decimals, first move the decimal point in the divisor to the right until it becomes a whole number. Then, move the decimal point in the dividend the same number of places and write the decimal point directly above the dividend. Divide the two numbers as if they were whole numbers, treating the decimal point as already in its proper place.

## Related Technology Terms

• Binary
• Base-10
• Digit
• Place Value
• Floating Point