Vertical Number Line

A number line with the numbers placed up to down in decreasing order is called a vertical number line. It has the origin, 0 in the middle, positive numbers (1, 2, 3, …..) above 0, and negative numbers (……., -3, -2, -1) below 0. We can easily relate it to the markings in a thermometer.

The above diagram shows a vertical number line with integers from -10 to 10.

-10 < -9 < -8 <… < 0 < …< 8 < 9 < 10

Sometimes students prefer to use a vertical number line compared to a traditional number line to perform various arithmetic operations, graphing, and rounding real numbers, including integers, decimals, and fractions. They also represent quantities with positive and negative values, such as credits or debits, temperature above or below zero, and elevation above or below sea level.

Representing Numbers Using Vertical Number Line

To represent a number on a vertical number line, we follow the following steps:

Step 1: First, the number is identified, whether it is a positive or a negative number.

Step 2: A positive number is marked above 0 by moving up the steps above 0. Similarly, a negative number is marked below 0 by moving down the number of steps starting from 0.

For example, let us locate the numbers 8 and (-5) on the vertical number line.

As 8 is a positive number, we find it by moving 8 steps above 0. In contrast, (-5) being negative, we find it by moving 5 steps below 0.

Rounding Numbers Using Vertical Number Line

A vertical number line can round a real number to its nearest specific place value (hundred, ten, one, tenth, hundredth, etc.)

Whole Number

For example, let us round 182 to its nearest hundred and ten.

182 is written using a place value chart below.

Nearest Hundred

As 182 lies between 100 and 200, by rounding 182 to its nearest hundred, we decide whether it is closer to 100 or 200.

Step 1:  An open vertical number line with numbers from 100 to 200 is drawn, with the starting number 100, ending number 200, and the middle point 150.

Step 2: As 5 < 8, 150 < 182, thus 182 lies above 150 on the vertical number line.

As 182 is closer to 200 than 100, 182 is rounded up to its nearest hundred, 200.

Nearest Ten

As 182 exists between 180 and 190, rounding 182 to its nearest ten shows whether it is closer to 180 or 190.

Step 1: First, we draw an open vertical number line with numbers from 180 to 190, with 185 as the middle number.

Step 2: Since 2 < 5, 182 < 185, 182 is marked below 185.

Thus 182 is closer to 180 than 190, it is rounded down to its nearest ten to get 180.

Decimal Number

Let us round the decimal number 3.827 to its nearest one, tenth, and hundredth.

First, 3.827 is written using a place value chart.

Nearest One

As 3.827 lies between 3 and 4, rounding 3.827 helps us to decide if it is closer to 4 or 3.

Step 1: An open vertical number line is drawn with the numbers from 3 to 4, where 3, 4, and the middle number 3.5 are marked.

Step 2:  Since 0.8 > 0.5, 3.827 > 3.5, 3.827 lies above 3.5 in the open vertical number line.

3.827 is closer to 4 than 3, so it is rounded to its nearest one, 4.

Nearest Tenth

Considering the decimal numbers, including tenths between 3 and 4, 3.827 lies between 3.8 and 3.9. Rounding 3.827 to its nearest tenth means finding if it is closer to 3.8 or 3.9.

Step 1: Let us draw an open vertical number line with the numbers from 3.8 to 3.9 and 3.85 as the middle number.

Step 2: Now, as 0.02 < 0.05, so 3.827 < 3.85, and it lies below 3.85.

As 3.827 is closer to 3.8 than 3.9, 3.827 is rounded down to its nearest tenth, 3.8.

Nearest Hundredth

On considering the decimal numbers with digits in the hundredth place between 3 and 4, 3.827 is found to exist specifically between 3.82 and 3.83. Here, we will find whether 3.827 is closer to 3.82 or 3.83.

Step 1: An open vertical number line with the numbers from 3.82 to 3.83 is drawn, and 3.82, 3.83, and 3.825 (the middle number) are marked.

Step 2: Since 0.007 > 0.005, 3.827 > 3.825, 3.827 lies above 3.825 on the vertical number line.

From the diagram above, 3.827 is found to be closer to 3.83 than 3.82

Thus 3.827 is rounded up to its nearest hundredth, 3.83.

Here we have provided a blank vertical number line for students to use.