When learning about mathematics, it’s important to understand the difference between real numbers and integers. Real numbers include decimals and fractions, while integers are whole numbers without decimals. Integers can be positive or negative, while real numbers always have a positive value. Understanding these distinctions is essential for mastering math concepts.

## What are Real Numbers?

Real numbers are numbers that can be found on the number line. Real numbers can be positive or negative, and they can be whole numbers or fractions.

- Real numbers can also be irrational numbers, which are numbers that cannot be expressed as a fraction. Real numbers are important in mathematics because they can be used to represent many different things.
- For example, Real numbers can be used to represent the amount of money in a bank account, the temperature outside, or the speed of a car. Real numbers are also important in algebra and calculus.
- Algebra is a branch of mathematics that uses real numbers to represent variables and equations. Calculus is a branch of mathematics that uses real numbers to find rates of change. Real numbers are an essential part of mathematics, and they can be used to represent many different things.

## What are Integers?

Integers are Whole Numbers that can be positive or negative. Integers include zero, and they are the set of numbers {-3,-2,-1,0,1,2,3,…}. Integers are used in everyday life, especially when talking about money.

- Integers are also used in computers because they can store data more efficiently. Integers can be added, subtracted, multiplied, and divided. The operations follow the same rules as with whole numbers.
- Integers can also be compared using the signs < (less than), > (greater than), = (equal to), ≥ (greater than or equal to), and ≤ (less than or equal to). Integers can be sequenced on a number line from left to right or from right to left.
- The integers get larger as you move to the right on the number line, and they get smaller as you move to the left. That’s all there is to integers! They’re not so scary after all!

## Difference between Real Numbers and Integers

- Real numbers and integers are two types of numbers that are often used interchangeably, but there is a key difference between the two. Real numbers include any number that can be expressed on the number line, including fractions and decimals.
- Integers are whole numbers that can be positive, negative, or zero. In other words, all integers are real numbers, but not all real numbers are integers. This can be a confusing concept, but it’s important to remember when working with numbers.
- Real numbers can be used in many different ways, but they don’t always have the same properties as integers. For example, adding two real numbers can result in a fraction or decimal, but adding two integers will always result in an integer. This is just one way that real numbers and integers differ, so it’s important to keep this distinction in mind.

## Conclusion

Integers are whole numbers, while real numbers include fractions and decimals. The set of all integers is a subset of the set of all real numbers. This means that every integer is a real number, but not every real number is an integer. For example, the number 1.5 is a real number, but it is not an integer because it includes a fractional component. When working with mathematical equations or problems, it’s important to be clear about which type of number you’re using so that you get the correct answer!