What is an Integer?

S3-SA4-0356

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

An integer is a whole number that can be positive, negative, or zero. It does not have any fractional or decimal parts. Think of them as complete numbers without any 'pieces' leftover.

Simple Example

Quick Example

Imagine your cricket team's score. If your team scores 250 runs, that's a positive integer (+250). If the opponent team loses 5 wickets, that can be represented as a negative integer (-5) when tracking changes. Zero runs is also an integer.

Worked Example

Step-by-Step

PROBLEM: Identify all integers from the following list: -7, 3.5, 0, 100, 1/2, -25.

STEP 1: Understand what an integer is. It's a whole number, positive, negative, or zero, with no fractions or decimals.
---STEP 2: Look at -7. It's a whole number and negative. So, -7 is an integer.
---STEP 3: Look at 3.5. It has a decimal part. So, 3.5 is NOT an integer.
---STEP 4: Look at 0. It's a whole number and zero. So, 0 is an integer.
---STEP 5: Look at 100. It's a whole number and positive. So, 100 is an integer.
---STEP 6: Look at 1/2. It's a fraction. So, 1/2 is NOT an integer.
---STEP 7: Look at -25. It's a whole number and negative. So, -25 is an integer.
---ANSWER: The integers from the list are -7, 0, 100, -25.

Why It Matters

Integers are fundamental building blocks for almost all calculations in science and technology. From predicting weather patterns (Physics) to managing your phone's data usage (Computer Science) or calculating profits in a business (Economics), integers are everywhere. They are crucial for engineers designing buildings and for AI/ML models that process numerical data.

Common Mistakes

MISTAKE: Thinking that fractions or decimals are integers. E.g., believing 1.5 or 3/4 are integers. | CORRECTION: Integers are strictly whole numbers. They do not have any parts after the decimal point or as a fraction.

MISTAKE: Forgetting that zero is an integer. E.g., only considering positive or negative numbers. | CORRECTION: Zero is a very important integer, separating positive and negative integers on the number line.

MISTAKE: Confusing natural numbers or whole numbers with integers. E.g., thinking -5 is not an integer because it's not a 'counting' number. | CORRECTION: Natural numbers (1, 2, 3...) are positive integers. Whole numbers (0, 1, 2, 3...) include zero and positive integers. Integers include positive, negative, AND zero whole numbers.

Practice Questions

Try It Yourself

QUESTION: Is 15 an integer? | ANSWER: Yes

QUESTION: Which of these are NOT integers: -10, 4.2, 0, 200, -1/3? | ANSWER: 4.2, -1/3

QUESTION: Your savings account has Rs. 5000. You withdraw Rs. 1500. Then you deposit Rs. 700. Represent these transactions as integers and find your final balance. | ANSWER: Initial: +5000. Withdrawal: -1500. Deposit: +700. Final balance: 5000 - 1500 + 700 = Rs. 4200.

MCQ

Quick Quiz

Which of the following is NOT an integer?

-100

2026-05-02T00:00:00.000Z

The Correct Answer Is:

Option C (5/2) is a fraction, which means it is not a whole number. Integers are whole numbers (positive, negative, or zero) without any fractional or decimal parts.

Real World Connection

In the Real World

When you check the temperature in Delhi, it might be 35 degrees Celsius (+35) in summer or -2 degrees Celsius (-2) in winter. These are integers. Even your bank balance on a UPI app uses integers to show how much money you have (+Rs. 10,000) or if you've gone into an overdraft (-Rs. 500).

Key Vocabulary

Key Terms

POSITIVE INTEGER: A whole number greater than zero, like 1, 2, 3... | NEGATIVE INTEGER: A whole number less than zero, like -1, -2, -3... | ZERO: The integer that is neither positive nor negative. | WHOLE NUMBERS: The set of numbers 0, 1, 2, 3... (all non-negative integers).

What's Next

What to Learn Next

Great job understanding integers! Next, you can learn about 'Operations on Integers' like addition, subtraction, multiplication, and division. This will show you how to use integers in real calculations and solve more complex problems.