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V.3 Put decimal numbers in order

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What does it mean to order decimal numbers?

Ordering decimal numbers means arranging them from least to greatest or from greatest to least by comparing their values.

Examples:
  • Least to greatest: 0.25, 0.36, 0.4
  • Greatest to least: 0.4, 0.36, 0.25
Note

When ordering decimals, always pay attention to the place value of each digit—tenths, hundredths, thousandths, and so on.

How to compare and order decimal numbers

To compare decimals, line up the digits by their decimal points and look at each place value from left to right until you find a difference.

Steps:
  • Write the numbers vertically, lining up the decimal points.
  • Add zeros if necessary so each number has the same number of decimal places.
  • Compare the digits in each place value from left to right.
  • Arrange the numbers in the correct order—least to greatest or greatest to least.
Note

Adding zeros after the last digit does not change a number’s value. For example, 0.5 = 0.50 = 0.500.

Understanding place value in decimals

Each digit in a decimal number has a specific value based on its position. The place value tells how much each digit is worth.

Example:
  • In 3.472, the 4 is in the tenths place, the 7 is in the hundredths place, and the 2 is in the thousandths place.
Note

The farther a digit is to the right of the decimal point, the smaller its value becomes.

Tips for putting decimals in order

When decimals look tricky, rewrite them so that each number has the same number of decimal places before comparing.

Examples:
  • Least to greatest: 2.305, 2.350, 2.400
  • Greatest to least: 2.400, 2.350, 2.305
  • Least to greatest: 0.600, 0.602, 0.620
  • Greatest to least: 0.620, 0.602, 0.600
Note

It helps to think of decimals as fractions with denominators of 10, 100, or 1,000. For example, 0.4 = 4/10 and 0.36 = 36/100.

Checking your work

After ordering decimals, read your list from left to right to see if the numbers increase or decrease correctly.

Examples:
  • Least to greatest: 1.25, 1.3, 1.48, 1.5
  • Greatest to least: 1.5, 1.48, 1.3, 1.25
Note

If a number seems out of order, double-check your comparison by aligning decimal points again.