What are Integers on a Number Line? (Examples) - BYJUS

# Integers on the Number Line and their Comparison

Integers are numbers that do not have a fractional component. Integers range from negative numbers to positive numbers and include zero. Here we will learn to represent integers on a number line and use this concept to compare two integers with each other....Read MoreRead Less

## What are Positive Numbers?

Positive numbers are whole numbers greater than 0. These numbers can be written with or without a positive sign or a plus sign, “+”.

+ 1, 96, + 26, 25000 are all examples of positive numbers.

## What are Negative Numbers?

Negative numbers are opposites of whole numbers excluding 0 on the number line. These numbers are written with negative sign or a minus sign, “.

-1, -96, -36, and -45634 are written with a minus sign and are negative numbers.

Example:

A footballer scored 5 goals in a game. We use a positive number to indicate the situation so the five goals are represented as +5 or 5 goals. Very cold temperatures are represented using negative numbers such as -3 degree Fahrenheit, -10 degrees Fahrenheit, etc.

## What are Integers?

Integers are the set of numbers such as … -2, -1, 0, 1, 2, … The integers consist of negative numbers, “0” and positive numbers. Integers do not have any fractional or decimal parts.

Graph of integers and their opposite.

A number is known as an opposite of another number if both the numbers are at the same distance from 0 on the number line. For example, 7 and -7 are both equidistant from 0, and hence are opposite to each other.

## Comparison of Integers on the Number line

On a horizontal number line, numbers to the left of the 0 are less than the numbers on the right. On a vertical line the numbers below the 0 are less than the numbers above.

For example, we compare 1 and -5 on a horizontal number line by graphing both these numbers on the number line.

1 is to the right of -5. This only means that 1 is greater than -5.

Again, we can compare -2  and -4  on the vertical number line after adding these numbers at appropriate points on the number line.

-4 is below -2, which only indicates, -4 is smaller or lesser than -2.

## Solved Examples on Integers

Example 1: Plot the number 3 and opposite of integer 3 on a number line.

Solution:

Draw a horizontal number line. Mark the number 3 on the number line. Now count 3 in the opposite direction of 0, which is to the left. You will reach the point that represents -3. Hence -3 is at the same distance as 3 is from 0, but in the opposite direction. Hence, -3 is the opposite of 3 as shown in the diagram.

Example 2: Represents these situations using a positive or negative integer.

1. A savings account earns interest $15. 2.A student loses 6 points for saying the wrong answer. 3. A man climbed 5000 feet on a mountain. Solution: 1. A savings account earns$15, meaning the number is located to the right of the 0 on the number line. This shows a number greater than 0. Therefore, +15 or 15, is the required integer.
2.A student loses 6 points for saying the wrong answer. This shows a number less than 0. Therefore, -6 on the left side of the 0 on the number line, is the required integer.
3. A man climbed 5000 feet on a mountain. This shows a number greater than 0. Therefore, +5000 or 5000 is the required integer.

Example 3: Compare the given integers -5, 3, 0, -3, 4 and order them from the least to the greatest on a number line.

Graph each integer on a number line.

Write the integers as they appear on the number line from left to right.

So, the order from the least to the greatest integer is -5, -3, 0, 3, 4.

Example 4: David was playing with his brother. Both of them have a few marbles and they decide to play a game. In the first round, David loses 3 marbles. In the second round, he won 5 marbles. Write an integer that represents the marbles that were either lost or won by David.

Solution:

In the first round, David lost 3 marbles. As this is a reduction in the number of marbles David had, it is represented as -3, a negative integer.

In the second round, he won 5 marbles, this is represented by +5 or 5, a positive integer.

Yes, all negative numbers are less than 0, as they lie to the left of 0 on a number line.

For example, let’s compare 0 and -4.

The integer 0 is greater than -4. Because 0 is on the right of -4 on the number line.

Yes, all the positive integers lie to the right of all the negative integers on a number line. Therefore, negative integers are always less than positive integers.

The fact is that “0” is neither a positive nor negative integer. However, the number zero makes it easier to distinguish between positive integers on the right of it, and negative numbers on the left of it.