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A decimal number is a number that is based on the number 10 and contains a **decimal point**. It consists of a whole number part and a fractional part, separated by the **decimal point**.

The position of each digit in a decimal number is important and represents its **place value**. As we move left, each position is 10 times bigger, while as we move right, each position is 10 times smaller.

**Decimal numbers** can be as large or as small as desired, using the **decimal point** to indicate values greater than one or less than one. The decimal point is the most important part of a decimal number as it indicates the position of the ones digit.

Decimals are commonly used in various applications, such as monetary transactions, weight measurements, and scientific calculations.

## Types of Decimal Numbers

**Decimal numbers** can be classified into different types. Understanding these types is essential for working with decimals effectively.

### Recurring Decimals

**Recurring decimals**, also known as repeating decimals, are **decimal numbers** that have a pattern that repeats indefinitely. For example, the decimal representation of one-third is 0.3333…, where the digit 3 repeats infinitely. The ellipsis (…) indicates the repetition. **Recurring decimals** can be represented using a bar notation, such as 0.3̅ to represent 0.3333….

### Non-recurring Decimals

**Non-recurring decimals**, also known as terminating decimals, are decimal numbers that have a finite number of digits after the decimal point. These decimals can be written using a fixed number of decimal places. For example, the decimal representation of three-fourths is 0.75, where there are two digits after the decimal point.

### Decimal Fractions

Decimal fractions are decimal numbers that represent fractions with a denominator that is a power of ten. They can be thought of as fractions expressed in decimal form. For example, the decimal representation of one-half is 0.5, which is equivalent to the fraction 1/2. Decimal fractions can also be written as mixed numbers or improper fractions.

Converting a decimal to a **decimal fraction** involves determining the denominator based on the number of digits after the decimal point and placing the decimal number over the appropriate power of ten. This allows us to express decimal numbers as fractions and perform operations on them.

Understanding these different types of decimal numbers is crucial for performing calculations and solving problems involving decimals. They have various applications in everyday life, including measurements, financial transactions, and scientific calculations.

## Place Value Representation of Decimal Numbers

Decimal numbers are represented using the **place value** system. The position of each digit in a decimal number indicates its value. The decimal point separates the whole number part from the fractional part. As we move from left to right, each position is 10 times smaller than the previous position.

The first digit to the right of the decimal point represents tenths, the second digit represents hundredths, the third digit represents thousandths, and so on.

The **expanded form** of a decimal number shows the value of each digit based on its position. For example, in the decimal number 17.48, 17 is the whole number part and 48 is the decimal part.

The **place value** chart helps in understanding the powers of ten associated with each position.

### Place Value Chart for Decimal Numbers

Whole number part | Decimal part |
---|---|

10,000s | Thousandths |

1,000s | Hundredths |

100s | Tenths |

10s | Ones |

## Arithmetic Operations on Decimals

Decimal numbers offer a wide range of possibilities when it comes to arithmetic operations. From **addition** and **subtraction** to **multiplication** and **division**, these operations can be easily performed on decimal numbers with a few simple steps.

When adding or subtracting decimal numbers, it’s crucial to align the decimal points. This allows us to perform the operation as if there were no decimal points at all. For **multiplication**, the process is similar to that of whole numbers. However, the placement of the decimal point in the product is determined by the combined number of digits after the decimal point in the operands.

**Division** of decimal numbers requires an additional step. We need to move the decimal point in the divisor to make it a whole number and then proceed with the **division** operation. This ensures accurate results. Additionally, decimal numbers can also be converted into fractions. By writing the **expanded form** of the decimal number and simplifying the resulting fraction, we can obtain a precise representation of the decimal in fraction form.

Mastering these arithmetic operations on decimals allows us to effortlessly perform calculations involving **addition**, **subtraction**, **multiplication**, division, and even conversion to fractions. Understanding and applying these operations is essential when working with decimal numbers in various real-life scenarios.

## FAQ

### What is a decimal number?

A decimal number is a number that is based on the number 10 and contains a decimal point. It consists of a whole number part and a fractional part, separated by the decimal point.

### What are the types of decimal numbers?

Decimal numbers can be classified into different types. **Recurring decimals**, also known as repeating decimals, have a pattern that repeats indefinitely. **Non-recurring decimals**, also known as terminating decimals, have a finite number of digits after the decimal point. Decimal fractions are fractions with a denominator that is a power of ten.

### How are decimal numbers represented using the place value system?

The position of each digit in a decimal number indicates its value. The decimal point separates the whole number part from the fractional part. As we move from left to right, each position is 10 times smaller than the previous position. The first digit to the right of the decimal point represents tenths, the second digit represents hundredths, the third digit represents thousandths, and so on.

### What are the arithmetic operations that can be performed on decimal numbers?

Decimal numbers can undergo various arithmetic operations. **Addition** and **subtraction** of decimal numbers involve aligning the decimal points and performing the operation as if there were no decimal points. Multiplication of decimal numbers is similar to multiplication of whole numbers, with the decimal point placed in the product based on the number of digits after the decimal point in the operands. Division of decimal numbers requires moving the decimal point to make the divisor a whole number, and then performing the division operation. Decimal numbers can also be converted to fractions by writing the **expanded form** and simplifying the resulting fraction.