A visual depiction of numbers as they would appear on a line is called a number line. Numbers that are plotted on this line at equal intervals so that they may be compared with one another along an endless line that may stretch either horizontally or vertically are shown. When we travel from the left side of a horizontal number line toward the right side, the numbers become higher, and when we move from the right side toward the left side, the numbers get lower.
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What is a Number Line?
A number line is a graphical depiction of numbers that are shown in a straight line, either horizontally or vertically, and may be drawn in either direction. When we write down the numbers on a number line, it is much simpler for us to compare the numbers as well as carry out the fundamental arithmetic operations on them.
On a number line, zero (0) is believed to be the point at which the line begins. The numbers to the left of zero are considered to be negative numbers, whereas those to the right of zero are considered to be positive numbers.
Based on this, we can assert that the value of a number rises as it is moved to the right along a number line. This indicates that the numbers that can be found on the right are more than the numbers that can be found on the left. As an example, because 3 is located to the right of 1, it is greater than 1.
Putting numbers on a number line makes it much simpler to evaluate their relationship with one another. It is clear from the illustration that the integers on the left are less than those on the right, which shows that the left is less than the right. For instance, 0 is a smaller number than 1, -1 is a smaller number than 0, -2 is a smaller number than -1, and so on.
Comparing Numbers Utilizing Number Line
The first number is bigger than the second if it is located more to the right on the number line than the second (equivalently, the second is less than the first). The difference between them, measured as the first number less than the second, or as the absolute value of the second number less than the first, is the distance between them. Subtraction is the procedure of taking this difference.
Therefore, for instance, the magnitude of any other number is represented by the length of a line segment that begins at 0 and ends at some other number.
It is possible to add two numbers by “lifting” the length from 0 to one of the numbers, placing it down again with the end that was 0 placed on top of the other number, and then “set it down” again. This completes the addition.
You may multiply two integers like in the following example: Pick up the length from 0 to 5 and put it to the right of 5, then pick up that length again and put it to the right of the previous result since multiplying 5 by 3 is the same as multiplying 5+5+5. Since the procedure terminates at 15, we determine that 5×3 = 15. This results in a result that is 3 combined lengths of 5 each.
The division shown in the example below may be done as follows: The length from 0 to 2 is at the beginning of the length from 0 to 6, so divide 6 by 2- that is, to determine how many times 2 goes into 6 – pick up the former length and place it down again to the right of its original position, with the end that was previously at 0 now placed at 2, and then move the length to the right of its latest position once more.
In the length range of 0 to 6, this places the right end of length 2 at the right end. Two went into six three times since three lengths of two filled the length six (i.e., 6 2 = 3).
Negative and Positive Number Line
The two types of numbers displayed on a number line are positive and negative numbers, as was previously mentioned. Let’s study more about the positive and negative number lines in this session.
The section of the number line to the left of zero is known as a negative number line. Contrarily, the region to the right of zero is referred to as a positive number line since it only includes positive integers. It may be extended forever from either end.
No length restriction applies to number lines. It may be as little as the size of your notepad or as lengthy as it would take to circle the globe a million times. The negative and positive number lines each have the following characteristics.
- The right-hand numerals are worth more than the left-hand ones.
- The value of the left-hand numerals is less than that of the right-hand digits.
- The midpoint of the number line, or the point of origin, is 0 (zero).
The numerals are equally spaced apart. This implies that if you need to create a number line, you must use numbers that are properly placed in order. The format of a number line cannot be 1, 2, 5, 11, etc. A number line is usually formed with the appropriate spacing, such as 1, 3, 5, 7,… 99, or 5, 10, 15, 20,…
You will learn how to create/draw a number line in the part after this one when we explain this idea in more depth.
Read more >> What is a base 10? Understanding the Base-Ten System
How to Draw a Number Line?
Read this step-by-step guide written by our knowledgeable professors to assist you to comprehend number line principles quickly.
- Step 1: On a piece of paper, draw a straight line either horizontally or vertically (your option). At both ends, add two arrows. These arrows indicate that on the left and right sides, the line goes on forever.
- Step 2: The second step is the most important. To produce the marks on the number line, this step entails selecting the proper scale. For instance, you may choose a scale of 1 or 2 if you need to plot integers from 0 to 4. The numbers on the number line should be 0, 1, 2, 3, and 4 on a scale of 1. The numbers on the number line will be 0, 2, and 4 on a scale of 2. With an equal amount of intervals between the two numbers, pick your scale appropriately.
- Step 3: Once again, think about the 0–4 number line. As the interval has already been set to 1, the points will be 0, 1, 2, 3, and 4. All of these points are marked in the third stage. They will serve as markers.
- Step 4: The fourth and last step is to locate the desired number and highlight it using a circle.
This is a simple way to mark and draw any number on a number line. With the help of natural numbers, whole numbers, and integers, we have studied ideas relating to the number line. In the next courses, we will learn how to represent decimals and fractions on a line segment.
Number Line with Decimals
A dot separates the whole number portion of a decimal integer from the fractional portion. As in 13.3353, where 3353 is the fractional component of the decimal and 13 is the whole number portion. However, how should this be represented on the number line? To fully comprehend the notion of adding a decimal point to the number line, follow the instructions provided below.
How would you, for instance, depict 1.8 on a number line?
- Step 1: First, create a straight line.
- Step 2: Locate the entire number and the fractional number in step two. The full number in this instance is 1, while the fraction is 0.8. Mark the numbers with equal spacing following the whole number. Specifically, 0, 1, and 2.
- Step 3: Since 1.8 is situated between 1 and 2, we may make smaller marks with a value of 0.1 between them. From 1 to 2, create 10 equal intervals. As a result, the numbers between 1 and 2 are 1, 2, 3, etc.
- Step 4: Step 4 is to locate 1.8 and circle it.
Any decimal point should be shown on the number line in this manner. I assume everyone has a good understanding of the idea.
Final Words
What is a number line? The answer has been detailedly mentioned above. Hope that this information can be beneficial for you during the process of solving math problems. If you are planning to teach your kids about this essential topic, you can make your own collections of number line worksheets using our worksheet generator.
