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Order whole numbers

Ordering whole numbers means comparing three or more nonnegative whole numbers, typically through 100,000, and arranging them from least to greatest or greatest to least. The reasoning depends on place value: compare the greatest place first, then move right only when preceding digits are equal; a number line provides a corresponding magnitude representation and helps distinguish digit position from digit value. Decimals, fractions, negative numbers, and numbers beyond this range are not included.

Detailed Explanation: Order whole numbers

To order whole numbers, compare their place values from left to right.

  1. Compare the greatest place first.
  2. If the digits are equal, compare the next place.
  3. Keep moving right until the digits are different.
  4. Arrange the numbers from least to greatest or greatest to least.

Example: Order these numbers from least to greatest:

42,305,24,530,42,350,9,99942{,}305,\quad 24{,}530,\quad 42{,}350,\quad 9{,}999

First, compare the ten-thousands digits:

  • 9,9999{,}999 has 00 ten-thousands.
  • 24,53024{,}530 has 22 ten-thousands.
  • 42,30542{,}305 and 42,35042{,}350 each have 44 ten-thousands.

So far:

9,999<24,530<42,305, 42,3509{,}999 < 24{,}530 < 42{,}305,\ 42{,}350

Now compare 42,30542{,}305 and 42,35042{,}350. Their ten-thousands, thousands, and hundreds digits are equal. Compare the tens digits:

  • 42,30542{,}305 has 00 tens.
  • 42,35042{,}350 has 55 tens.

Therefore, 42,30542{,}305 is less than 42,35042{,}350.

The numbers from least to greatest are:

9,999,24,530,42,305,42,350\boxed{9{,}999,\quad 24{,}530,\quad 42{,}305,\quad 42{,}350}

On a number line, the numbers farther to the left are smaller, and the numbers farther to the right are greater.

Learn by doing: Order whole numbers

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    Number Sense - Ordering 4 Integers (descending)

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