# What Is a Number Line?

A number line is a visual representation of the positive and negative numbers and zero.

Note: The number line goes on left and right forever.

# Representing Numbers on a Number Line

A number line allows all numbers to be represented.

Usually only integers are marked on a number line. The marks represent integers, such as -1 and 2 shown below:

Other numbers, that include fractions, can be represented in between the marks, such as -2.5 and 3/2 shown below:

# Ordering of Numbers

The further right on the number line a number is, the greater it is. The further left on the number line a number is, the smaller it is:

This means that:

• any number is greater than any integer to its left.
• any number is less than any integer to its right.
For example,

• 3 is greater than 1.
• -1 is less than 1.

# Using the Number Line

A number line can be used to see how to add and subtract numbers.

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# ABSOLUTE NUMBERS AND THE NUMBER LINE

The absolute value, or modulus, of a number is the non-negative value of the number without regard to its sign.

The absolute value of a number is denoted by || either side of the number.

The absolute value of a positive number is just that number:

The absolute value of a negative number is the non-negative value of that number. It is that number with the minus sign ( - ) removed:

On a number line, the absolute value of a number is given by its distance from zero.

It can be seen that both 3 and -3 are 3 away from zero, and so both have an absolute value of 3: