The arrangement is a very important concept in mathematics. We will use this concept to find the median, arrange the terms of sequence, and other many fields we solve problems after arranging the data.

In this article, we will discuss the best way to arrange the data and solve different types of the data set. We will also discuss real-life applications and mathematical problems where arranging data is very important for researchers.

## Arranging the data:

The arrangement of the data set is carried out in two ways.

**INCREASING ORDER**

In increasing order, we arrange the data from smaller to larger values. In this way, the first data value is the smartest and the last value is the largest value of the data. This arrangement of the data is called ascending order.

**DECREASING ORDER**

In decreasing order, we arrange the data from a larger value to a smaller one. In this way, the first data value is the largest and the last value is the smallest value of the data. This arrangement of the data is called descending order.

## Data type:

In the ordering of data, we will data value in the form of a percentage, decimal, or fraction. We have different ways to arrange the data from least to greater or in a reverse way from greater to smaller.

### 1. Percentage method:

The first method is to compare the given data with each other by converting the data set into the form of a percentage.

**Example 1:**

Arrange the data values 8, 2.8, 20 %, and 4/5 from least to greater.

**Solution:**

**Step 1: **First of all, we have to convert all values in the form of percentage

8 = 800 %

2.8 = 280 %

4/5 = 80 %

20 % = 20 %

**Step 2:** Now we will understand that if the data value has a minimum value, it is replaced 1^{st} and move in increasing percentage.

20 % < 80 % < 280 % < 800 %

Replace the original values

20 % < 4/5 < 2.8 < 8

So least to greater values are in the form of

**20 %, 4/5, 2.8, 8**

You can arrange any data values easily and quickly by using a least to greater calculator

### 2. Decimal method:

In the decimal method, we have to change all the observation values in the form of a decimal. After converting all the data into decimals, we can compare them easily and arrange the data in ascending and descending forms.

#### · Converting percentage into decimal:

We can convert the percentage value into a decimal by dividing the percentage values by 100.

For e.g. 20 % can be written in decimal form as 20/100 = 0.20

Similarly, we can change any percentage value into a decimal by just dividing by 100.

#### · Converting fraction into decimal:

We can convert any fraction input value by dividing the numerator by the denominator. For example, if we write a fraction value 5/2 in the decimal form just carry the division method after the decimal and we obtain the answer 2.5 in the form of a decimal.

In the same way, we can covert any fraction in the form of decimal and we easily use the data for comparison.

#### · Converting the Whole numbers into decimal:

We know that every whole number can be converted into the form of a decimal by just replacing a decimal at the end of every whole number.

For example, 19 is a whole number we can convert it to decimal by just replacing decimal at the end of a value like 19.0.

**Example 2:**

Arrange the data values 18, 0.9, 30%, 4/5, and 9% from least to greater.

**Solution:**

**Step 1: **First of all, we have to change all inputs in the form of a decimal.

**Step 2:** For the whole number

18 is a whole number so the decimal form is 18.0

0.8 is already in the form of decimal no need to change it.

**Step 3: **Percentage to decimal

30% and 9% can be changed in decimal form by divided by 100.

30 % = 0.3

And

9% = 0.09

**Step 4: **Fraction to decimal

4/5 is in the form of a fraction we can change it by the division method.

4/5 =0.8

**Step 5: **Now compare all decimal values and arrange from least to greater we obtain

**9 %, 30%, 4/5, 0.9, 18**

### 3. Fraction method:

In the fraction method, we change all data values in fractions and make the denominator the same to compare them.

#### · Converting percentage into a fraction:

We can convert the percentage value into a fraction by writing 100 in the denominator. After that, we can also simplify the fraction.

For e.g. 25 % can be written in decimal form as 25/100 = 1/4

Similarly, we can change any percentage into a fraction just by writing 100 in the denominator.

#### · Converting decimal into a fraction:

We can convert any decimal input value into a fraction by removing the decimal and counting the number of digits after the decimal and then writing the denominator. For example, if we write a want to convert 2.13 decimal value into a fraction that can be in the form of 213/100.

#### · Converting the Whole numbers into a fraction:

We know that every whole number can be converted into the form of a fraction by just replacing a 1 in the denominator of every whole number.

For example, 19 is a whole number we can convert it to a fraction by just replacing 1 in the denominator of 19 like 19/1.

**Example 3:**

Write the values 2, 0.7, 10%, 9/5, and 21/2 from least to greater form.

Solution:

**Step 1: **Change all the data into fraction form one by one

2 = 2/1

0.7 = 7/10

10 % = 10/100 = 1/10

9/5 and 21/2 not need to convert.

**Step 2: **Make the denominator the same by taking **LCM of (1, 10, 10, 5, 2) = 10**

Change all the values into the same denominator.

2/1 = 20/10

7/10 and 1/10 do not need to change

9/5 = 18/10

21/2 = 105/10

So, the value with smaller is replaced as 1^{st} and moves with the increasing nominator.

1/10, 7/10, 18/10, 21/10, 105/10

So, we obtain the value arranged from least to greater.

0.1, 0,7, 9/5, 2, 21/2

## Summary:

In this article, we have learned different methods to arrange the data values in our desired form. You can easily arrange the data set according to the given situation to make the solution optimize.