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# Number Line

A number line offers a visual representation of real numbers on a straight line. It is often used to compare and order integers that are placed at equal intervals.

The following is an example of a number line:

It is common to mark the middle of a number line with the number $0$ (often referred to as the point of origin) then place positive numbers to the right of the $0$ and negative numbers to the left. Arrows pointing to the left and right on the ends of the number line show that the line continues in both directions.

## Integers on the number line

Integers represented on a number line are whole numbers as well as their opposites (negative numbers that are the same distance from $0$ on the number line). Negative integers are listed to the left of the $0$ , while positive integers are listed to the right of the $0$ .

On the number line above, both $5$ and $-5$ are integers. They are also opposites because they are the same number of units from $0$ . On the other hand, $-4$ and 1 are not opposites because they are $4$ units and $1$ unit from $0$ , respectively.

It's good to note that, in addition to integers, you can find fractions, decimals, rational numbers, irrational numbers, and more represented on a number line.

## Intervals on the number line

Intervals are all of the numbers located between two given numbers on a number line. The example below "zooms in" to look at numbers on the negative side of the number line between $-1.4$ and $0.8$ . These numbers are represented as decimals:

Just as you can find number lines that "zoom in" on decimals, you can find number lines that "zoom out" to look at intervals like $5s$ , $10s$ , and larger. The following number line represents a larger interval with integers between $0$ and $400$ :

## Comparing and ordering numbers on a number line

Positive numbers on a number line (those to the right of the $0$ ) increase in value as they move farther right. On the other hand, negative numbers (those to the left of the $0$ ) decrease in value as they move farther to the left.

If you're comparing and ordering numbers on a number line, you'll want to remember that numbers to the right are larger than numbers to the left. In other words, $3$ is larger than $2$ , which is larger than $1$ , which is larger than $0$ , which is larger than $-1$ , etc.

## Practice questions on the number line

a. What happens to the value of numbers that move to the right on a number line?

They increase in value

b. What are $-4$ and $4$ considered on the number line?

Opposites

c. Compare the integers $-3$ and $-2$ . Which is larger?

$-2$

d. Can $5.6$ be represented on a number line?

Yes, decimals can be represented on a number line.

e. Place this set of integers in order from smallest to largest: $-4,5,-1,-7,0,3,6$

$-7,-4,-1,0,3,5,6$

f. Where are positive and negative numbers found in relation to 0 on a number line?

Negative numbers to the left and positive numbers to the right.

## Get help learning about the number line

There are many aspects of the number line to explore, including intervals, the types of numbers that can be found on the line, and the manner in which numbers can be compared and ordered. As your student learns more about the number line, they might develop questions. Working with a tutor can help them gain the clarity they need. Learn about the perks of taking part in tutoring by getting in touch with the Educational Directors at Varsity Tutors today.

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