How to Order Fractions & Decimals From Least to Greatest

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It is practically impossible to order fractions and decimals from least to greatest without either converting the fractions to decimals or vice versa. Converting the fractions to decimals is usually easier because you don't have to worry about finding the lowest common denominator of all the fractions before ordering. After you have converted everything to decimals, order the numbers the same way you order words alphabetically: began at the first unit, order from least to greatest, then move to the next unit and repeat the procedure.

  • Identify the decimal number in the series of numbers with the most units after the decimal point. For example, in the series of numbers 0.255, 2/9, 1/4, 0.8, 4/15 and 0.305, the decimal numbers 0.305 and 0.255 have the most units after the decimal point, with three.

  • Rewrite each fraction in the series as a decimal by performing long division. Divide each fraction so that the decimal equivalent has the same number of decimal units after the decimal point as the longest number or numbers, which you identified in Step 1. In the above example, you would rewrite 1/4 as 0.250, 2/9 as 0.222 and 4/15 as 0.267.

  • Order numbers from left to right based on the value of their leftmost unit, from least to greatest. If two numbers have the same value in their leftmost unit, ignore them until later. In the above example, all numbers have a leftmost unit of 0, so we cannot order them yet.

  • Move to the next unit over and order terms that have the same leftmost unit according their second unit value, again from least to greatest. In the above example, we would order the series 0.255, 0.222, 0.267, 0.250, 0.305, 0.8. Again, ignore terms that share the same second unit; you will order them in later steps.

  • Move to the next unit over and repeat the procedure of ordering them from least to greatest value for that unit until you have reached the final decimal value. In the above example, you would reorder the series 0.222, 0.255, 0.250, 0.267, 0.305, 0.8 and then move to the next unit and reorder the series 0.222, 0.250, 0.255, 0.267, 0.305, 0.8.

  • Replace the fractions you converted to decimals in Step 2 with their fractional equivalents. In the above example, you would rewrite the series as 2/9, 1/4, 0.255, 4/15, 0.305, 0.8.

References

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