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Ordering Decimals Calculator

Created by Luis Hoyos
Reviewed by Komal Rafay
Last updated: Jan 18, 2024


Don't waste more time manually calculating the order of decimal numbers, and use this tool! It has many different features, such as:

  • Comparing and ordering decimals and fractions.
  • Comparing expressions in not-yet-calculated form. Say:
    • (3 + 12 × 3);
    • (2 + 6.43)/4; and
    • (-1) × (13.1 - 5).
  • Obviously, ordering integer numbers.

You can use this ordering decimals calculator for any of the above types of expressions, even combining them.

Comparing and ordering decimals

Comparing and ordering decimals is almost the same history as for integer numbers, but we must take some additional considerations for the comparison of two decimals:

  • The greatest number will be the one with the highest integer part, no matter the decimals. For example, 23.1215 > 22.1215 as 23 > 22.
  • If both integers are the same, compare the decimals one by one from left to right until finding one larger than its corresponding rival.

For example, let's compare 56.46543 vs. 56.46912:

  1. First, we note both integers (56) are equal. Therefore, we must compare the decimals;
  2. First decimals are the same (4 = 4);
  3. Second decimals are also equal (6 = 6);
  4. The third decimal of the first number is lower than that of the second one (5 < 9). Therefore, 56.46543 is lower than 56.46912.

If the number of decimals is different, you could face a situation in which the one with fewer decimals shares the decimals of the other number. In that case, the greater will be the one with more decimals, as those additional decimals make it larger. For example, we know that 37.46563 > 37.46 because the first two decimals are the same, but 37.46563 has some decimals after that.

Once you know how to compare two decimals, you can use that superpower to order large sets of them using any of the methods explained in our ordering numbers calculator article.

Other calculators to order decimals, fractions, and more

FAQ

How do I order decimals and fractions from least to greatest?

Use the following methods to order decimals and fractions:

  • For decimals:
    • The greatest is that with the greater integer (e.g., 23.1215 > 22.1215).
    • If both integers are equal, compare the decimals one by one from left to right until finding the larger one. E.g., 54.6795 > 54.67341 because of the third decimals (9 > 3).
  • For fractions, there are two ways:
    1. Convert them into decimals and use the method for ordering decimal numbers.
    2. Convert all elements into equivalent fractions with equal denominators. When the denominators are the same, the greater will be that with the larger numerator (i.e., 203/200 > 100/200).

How to order the fractions 2/3, 3/7, and 4/8 from least to greatest?

To order the fractions 2/3, 3/7, and 4/8 from least to greatest:

  1. Convert the fractions into equivalent fractions with the same denominators.
    • 2/3 = 112/168;
    • 3/7 = 72/168; and
    • 4/8 = 84/168.
  2. The greater for two fractions with equal denominators will be the one with the greater numerator. Therefore: 72/168 < 84/168 < 112/168.
  3. Finally, convert each fraction into its original form. The order of the fractions from least to greatest is 3/7 < 4/8 < 2/3.
Luis Hoyos
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