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Math Calculators ▶ Least to Greatest Calculator

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**Table of Content**

An online least to greatest calculator is exclusively programmed to organize an unsorted list of numbers, decimals, percentages, and fractions in either ascending or descending order.

Read on to find a few informative concepts corresponding to data ordering!

In mathematical context, it is a handy practice to arrange the given data in a sorted way before you apply various operations to obtain the results. You must know the following terms to compile the information that is not uniformly distributed. Also, a least to greatest calculator is a best way to obtain a proper order of the numbers.

**Ascending Order:**

“A practice of ordering numbers from least to greatest is called ascending order.”

**Standard Form:**

The generic structure of ascending order is as follows:

**a<b<c<d<e<…**

**For example:**

5<6<7<8<10<…

**Descending Order:**

“The arrangement of numbers from greatest to least is known as descending order.”

**Standard Form:**

The general form of descending order is as follows:

**a>b>c>d>e>…**

**For example:**

9>6>2>1>0>…

A greatest to least calculator can arrange a given set of numbers from higher to lower one in a well organized way.

Numbers can be written in many forms like percentage, integers, whole numbers, fractions and decimals etc.That is why we should know the basic terms and conditions to keep in mind while we order numbers from least to greatest or greatest to least.

**Ordering Numbers (Integers):**

There can be many ways to order numbers from least to greatest or from greatest to least one. Comparing each number in a list with all others is a good practice. But if the list is very long, then it becomes a time consuming process. To avoid this, you should use sorting algorithm which states that:

**“Make a comparison of two consecutive numbers one after the other and replace their positions if they are in a wrong order”**

It is an easy practice to work on two numbers at a time instead of the whole list. Keep on considering the pairs and changing the positions of the numbers if required until the proper order is obtained.

**Ordering Decimals:**

The basic rule for ordering the decimal numbers is the same. For instance, just consider we have two numbers 2 and 3. It is very easy to say that 2 is smaller than 3. But the same case is not that easy if we get the numbers in the form of 1 / 2 and 2 / 3. This section is arranged to deal with such problems.

Now consider we have two decimal numbers. What we need to do is to start from the most left of both numbers and compare each single number. When you get an individual number in the decimal number that is greater than the number at the same position in the second decimal number, consider that decimal number to be the greatest one. However, a free least to greatest decimals calculator arranges a list of decimals numbers in a sorted order.

**Ordering Fractions:**

A simple way to order least to greatest fractions is to convert them into decimal numbers and recall the procedure for decimal numbers to order these numbers from least to greatest or vice versa. Well it seems simple but sometimes when we have fractions that gives an infinite sequence of decimal places when converted to decimal numbers, it becomes very difficult to obtain a precise order.

Here, you should adopt the use of equivalent fractions.

Multiply numerators and denominators of all fractions with the least common multiple to get the same denominator in all terms.

In case the numbers are coprime, choose a number to multiply upper and lower terms of fraction that can be the same for a single fraction but different for all fractions. Keep in mind you get the same denominator in all fractions.

To make things better, we will solve numerous examples to make your vision clear.

Sorting the numbers in order from least to greatest is an easy process if understood properly. Let us work on the following problems below:

**Problem # 01:**

Arrange the following decimals least to greatest:

**2.2356 , 2.2455**

**Solution:**

First, start from the most left and compare the first single digit in both numbers which is 2 as shown below:

**2.2356 and 2.2455**

Now move to the next one which is same in both numbers and is **2.**

**2.2356 and 2.2455**

Move to the third one digit in both numbers which is:

**2.2356 and 2.2455**

As we see that** 4 > 3**, so the second number is the greatest one.

**2.2356 < 2.2455**

Here, our free online least to greatest calculator gives the same results but in a span of seconds.

**Problem # 02:**

Arrange the following fractions least to greatest:

**2/3, 3/8**

**Solution:**

Applying the rule of equivalent fractions,m we have:

**2/5 = (2 * 8) / (5 * 8) = 16/4**0

**3/8 = (3 * 5) / (8 * 5) = 15/40**

As we see that first one is larger than the second one as **16 >15**. so ordering fractions from least to greatest:

**16/40>15/40**

Writing the original equations equivalent to these,we have:

**2/5>3/8**

**Problem # 03:**

Arrange the following numbers in order from least to greatest:

**21, 56, 2, 89, 7, 122**

**Solution:**

Now we will make pairs of consecutive numbers one after the other to simplify our calculations:

In the first pair **21, 56,** both numbers are in correct positions.

**21, 56, **2, 89, 7, 122

Next pair is **56, 2.** Note that 2 is smaller than 56. so they need to be replaced:

21, **56, 2,** 89, 7, 122

**21, 2, 56, 89, 7, 122**

Next pair is **56, 89**. See both the numbers are in correct least to greatest order.

Next Pair is **89, 7**. Since **7** is smaller than **89**, replace the numbers:

21, 2, 56, **89, 7**, 122

**21, 2, 56, 7, 89, 122**

Next pair is **89, 122** which is correct at all.

As we still see that all numbers are not ordered correctly, so repeat the process until we order the numbers from least to greatest.

**21, 2, 56, 7, 89, 122**

First pair is **21, 2**. Since **2** is greater than **21**, replace their positions:

**21, 2**, 56, 7, 89, 122

**2, 21, 56, 7, 89, 122**

Next pair is **21, 56** which is correctly ordered.

Now the next pair is **56, 7.** As we see that **7** is smaller than **56**, replace them:

2, 21, **56, 7,** 89, 122

**2, 21, 7, 56, 89, 122**

Now we see all next pairs are in correct order, but still **7** and **21** are not in good positions. Just replace them to get the final ordering numbers from least to greatest.

2, **21, 7,** 56, 89, 122

**2, 7, 21, 56, 89, 122**

As we see that apart from easiness, its a time consuming process. As time is money! That is why an online fractions least to greatest calculator is the best method to get proper order instantly.

Our calculator designed in such a way that it generates a well defined list of the un-sortd data in a sorted manner. What you need to do is:

- Write down the numbers either in the form of integers, fractions or percentages in the menu box.
- Select either “least to greatest” or greatest to least” from the next tab.
- Click ‘calculate’

**Output:**

The least to greatest calculator performs the following operations on input numbers given:

- Convert all the numbers into an easy format
- Make a proper list according to the choice you selected

The absolute value is the distance from the zero. It can not be taken as negative.

**For example:**

The absolute value of **5** is **5** and the absolute value of **-9** is also **9.**

The number **0.35** is bigger. This is due to the addition of an extra** 0.05** as **0.3 = 0.30.**

By default, it is always considered that more a number is greater with a negative sign, the more smaller it is.

**For example:**

**-2** is smaller than** -1**. Similarly, **-56** is smaller than **-9.**

In real life, absolute value corresponds to the difference between two points.

**For example:**

If you are running in a race of **50** candidates where all of them are running at a speed of **10mph** and you at **15mph,** it is more likely to say that you have more distance covered from the starting point than all others.

It is very important to write the numbers in order from least to greatest or greatest to least in accordance with the demand. In the field of data science, a vast use of online least to greatest calculator is adopted to maintain the data in a well organized way.

From the source of Wikipedia: Sorting, Insertion sort, Selection sort, Bubble sort, Merge sort, Quicksort

From the source of Khan Academy: Number concepts, Percentages, Rational number operations

From the source of Lumen Learning: Sorting Data, Filtering Data.

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