To order the numbers in descending or ascending order, put them in the least to greatest calculator. Show
Least to greatest calculator aka ordering fraction calculator orders fractions, decimals, and numbers in both ascending and descending manners. Ascending and descending ordersAscending order means the arrangement of values from least to greatest. Descending order means the arrangement of values from greatest to least. How to order numbers from least to greatest?To arrange number from least to greatest value aka ascending order, you have to
Example: Arrange the following fractions from least to greatest. 1/2, -3/4, -4/3,and 2/3 Solution: Step 1: Convert into decimals. = 0.5, -0.75, -1.33, and 0.667 Step 2: Identify the smallest value. = -1.33 Step 3: Similarly, Identify other values. = -1.33, -0.75, 0.5, 0.667 How to order numbers from greatest to least?To arrange number from greatest to least value aka descending order, you have to
Example:Arrange the following in descending order. 23, 676, 13, 87, and 99 Solution: Step 1: Identify the greatest value. = 676 Step 2: Similarly, Identify other values. = 676, 99, 87, 23, and 13 Created by Maciej Kowalski, PhD candidate Reviewed by Steven Wooding Last updated: Oct 01, 2022 Welcome to Omni's least to greatest calculator, where we'll help you put your numbers in order. In general, the task shouldn't be too tricky, but it can get messy if there are many entries or, even worse, if they are not yet calculated, i.e., they are some arithmetic expressions. Don't worry; with our tool, even ordering fractions and decimals from least to greatest will be super simple! Even better - when needed, our calculator can be turned to a number sorter from greatest to least (i.e., you can switch between ascending order and descending order). Let's jump straight into the article and begin the lesson! How to order numbers from least to greatestWhen we get a sequence of numbers Therefore, the real problem here is efficiency. Even though we know a brute-force way to order numbers from least to greatest, it may be important how fast we do it, especially in computer studies. As a consequence, several so-called sorting algorithms have been invented. We will now present one number sorter, which is easy and very popular. The idea behind bubble sort is simple: you compare pairs of numbers one after the other and swap their places if they're in the wrong order. In fact, we'll see that it's enough to check two consecutive elements at a time and repeat as long as needed. The steps of the algorithm are:
The above number sorter puts the entries in ascending order. Computer scientists say that, on average, the time it takes is equal to Before we finish the section, let us mention that the least to greatest calculator also admits entries in a not-yet-calculated form. In essence, if you need to compare, say, We'll see an example of bubble sort in action in the dedicated section. First, however, let's go through a few tips and tricks about sorting numbers. In particular, we focus on ordering fractions and decimals from least to greatest. Ordering decimals from least to greatestWhen dealing with
decimals or fractions, the basic rules are the same as with any other values: you have to compare the entries and put the numbers in order. However, while it's easy to see that We begin by ordering decimals from least to greatest since they're the simpler fractions. In fact, the story here is not too different from that of integers: we simply analyze the digits that appear in the numbers one by one, starting from the left side. For instance, if you want to compare Note that if both numbers are negative, then the process is the same, but the final conclusion is the opposite: if a digit of the first number is larger, the second number is the greater one. Also, remember that if one of the compared values has fewer digits
after the decimal dot Next, let's take a look at ordering fractions from least to greatest. Unfortunately, this task is slightly more complicated. Ordering fractions from least to greatestLet's take the example from the beginning of
the above section:
This way, we're back to the problem of ordering decimals from least to greatest, which is relatively simple. However, not all fractions have a nice decimal representation. Some of them are given by infinitely many digits after the dot! It seems like we need to find another way to compare them. We will use the so-called equivalent fractions. This method may take a little time with larger numbers, but in comparison to converting to decimals, it's a flawless algorithm for ordering fractions from least to greatest. We turn both entries into values with the same denominator. In fact, we can always multiply a fraction's nominator and denominator by an arbitrary number (but the same one, mind you!), and the value of the expression will stay the same. However, it's not so easy to find something which we can obtain in this way for both fractions. The brute-force method would be to multiply the two denominators. However, if you'd like to be a bit more subtle, you can choose their least common multiple. In fact, in our case, since the denominators are coprime (i.e., have no common factors), those two methods give the
same result: We know that
For
Now, we see that our initial task boiled down to comparing Hopefully, ordering decimals and fractions from least to greatest should be no biggie after reading the two sections. But what if we want to reverse the sorting? What if we want to put the numbers in order but from greatest to least? How do we do that? And does the least to greatest calculator have such an option? Good news, my dear padawan: the answers are, respectively, "It's easy" and "Of course!" All we need is in the next section. Ascending order vs. descending orderSo far, we've shown how to order numbers from least to greatest, i.e., in so-called ascending order. However, it so happens that we sometimes need to have the values sorted from greatest to least. We say then that we list the numbers in descending order (since the entries get lower with every step, just like descending a staircase). Fortunately, switching from ascending to descending order is super easy: we simply invert the inequality signs in our
calculations (or in algorithms, if we use them). For instance, we can change our bubble sort from the first section to make it a number sorter working from greatest to least. If we, again, have a list of entries
A piece of cake, isn't it? To finish the section, let us mention that our least to greatest calculator works, by default, in ascending order. However, we can easily convert it to a descending one: simply go to the advanced mode and choose the correct option under "Order." 🔎 Sorting and the related procedure of ranking the elements of a sample pop up in various branches of math, statistics, and science. If you want to cover some basic (yet fundamental!) notions, take a look at our median calculator and quartile calculator. If you want something more advanced, make sure to visit the Wilcoxon rank-sum test calculator. This concludes the theoretical part of the article. We hope you enjoyed it as much as we did and are ready to face a nice example that we've prepared especially for you! Example: using the least to greatest calculatorThere are not too many days left before Christmas, which can only mean one thing - it's time to look for presents for your family. With the pandemic raging on and a discussion about a lockdown reappearing you decide to choose the safest way: you go online shopping. You know what the first gift will be: a book. After all, these crazy times are quite good to catch up with your reading. You go to the website of your choice and type in the genre you know will agree with the person's taste. You see over a hundred results, so you decide to limit yourself to the top 10. Their prices are:
The titles don't tell you much, so you choose pragmatism over randomness and focus on the price. To help you decide, you'd like to put the numbers in order. Unfortunately, the site insists on listing the products according to how many copies the site sold recently. Good thing we have Omni's least to greatest calculator to take care of the problem! In our tool, we see variable fields marking consecutive entries of our dataset. We input the prices from the list above one by one. Note how initially we can only see eight boxes, but new ones appear the moment we seem to reach the limit (in fact, you can input up to fifty values). Also, observe how the least to greatest calculator shows the numbers in ascending order already for two entries and adjusts the results with every new value. Once we give the last one, we can read off the sorted list underneath. Before we finish for today, let's take the opportunity to see how to order the numbers from least to greatest by hand. We'll use the bubble number sorter introduced in the first section. We've already learned about ordering decimals from least to greatest in the
dedicated section, so we jump straight to the algorithm. We begin by taking the first entry and comparing it to the second. Since
Next, we move to the second number (which is now All in all, the first run through the dataset returns
We have made some (i.e., not zero) swaps, so we repeat the algorithm starting from the first entry. Just so that you don't fall asleep with descriptions of this repetitive procedure, we present below a table with the list at consecutive runs of the algorithm.
Observe how the 6th and 7th run return the same result. That is because, in the end, the algorithm needs one last iteration to be sure that we've indeed put the numbers in order. All in all, we see that once we sort the prices in ascending order, we get
Now we just need to make sure the sales tax is included, and then it's just a matter of deciding how much you want to spend. Does more expensive mean better? Maciej Kowalski, PhD candidate Values (enter up to 50 numbers) 5 number summaryBox plotCoefficient of variation… 34 more What is the order of numbers from least to greatest?If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
How do you write from least to greatest?Order the numbers from least to greatest.
Jot down the smallest number first—in our example, that's 11.47. Then, write out the next largest number, followed by the largest number. In our math problem, the final answer would be: 11.47, 12.45, and 12.457.
Is decreasing order least to greatest?What is descending order? When a series of data is arranged from high to low or largest to smallest, it means it is arranged is descending order, also known as decreasing order.
Which is a greater number?The number farthest to the right on the number line is the greater number.
|