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### Key Concepts

• Write rational numbers in decimal form: terminating decimals
• Write rational numbers in decimal form: repeating decimals
• Recognize rational numbers in decimal form

## 1.2Understand Rational Numbers

### What is a rational number?

A rational number is a number that is of the form , where p and q are integers and q ≠ 0. Rational numbers are denoted by Q .

How to identify rational numbers?

To identify if a number is rational or not, check the below conditions.

• It is represented in the form of p/q, where q≠0.
• The ratio p/q can be further simplified and represented in decimal form.
• All whole numbers are rational numbers

### Decimal Representation of Rational Numbers:

Rational numbers can be expressed in the form of decimal fractions.

A rational number can have two types of decimal representations:

• Terminating
• Non-terminating

#### Terminating decimals:

Terminating decimals are those numbers which come to an end after few repetitions after decimal point.

Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals.

#### Non terminating decimals (repeating):

Non terminating decimals are those which keep on continuing after decimal point. They do not come to an end or if they do it is after a long interval.

Example: 1/7= 0.1428571…. which is a non-terminating repeating decimal.

Example 1:

Convert the fraction, 5/8 to a decimal.

So,5/8 = 0.625. This is a terminating decimal.

Example 2:

Convert the fraction 7/12 to a decimal.

7/12= 0.583. This is a repeating decimal.

The bar over the number, in this case 3, indicates the number or block of numbers that repeat unendingly.

Example 3:

The length and breadth of a rectangle are 7.1 inches and 2.5 inches respectively. Determine whether the area of the rectangle is a terminating decimal or not.

Solution: Given, the length of rectangle is 7.1 inches and the breadth of rectangle = 2.5 inches.

Area of Rectangle = Length × Breadth = 7.1 inches × 2.5 inches =17.75 inches.

As the number of digits is finite after the decimal point, the area of rectangle is a terminating decimal expansion.

Example 4:

Write 5/3 in decimal form.

Using long division method, we will observe the steps in calculating 5/3

Therefore, 1.666… is a non-terminating repeating decimal and can be expressed as 1.6.

## Exercise:

Classify the following decimal fractions as terminating and non-terminating recurring decimals.

1. 0.777…
2. 0.777
3. 4.7182
4. 4.7182
5. 9.1651651…….
6. 9.165
7. 0.52888…….
8. 0.528
9. 72.13
10. 10.605

### What have we learnt:

• Understand the meaning of rational numbers
• Identify positive and negative integers
• Write the rational numbers in the form
• Write rational numbers as decimal form
• Differentiate between terminating and non-terminating decimals
• Solve problems on rational numbers

### Concept Map

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