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Order whole numbers

Ordering whole numbers through 1,000,000 involves comparing their place-value structure from the greatest place to the least, determining which number is greater, less, or equal, and arranging several numbers in ascending or descending order. A number line reinforces that greater numbers lie farther to the right, while attention to the highest differing digit prevents errors based only on a familiar digit or apparent length; decimals, negative numbers, and unrestrictedly large numbers are outside this scope.

Detailed Explanation: Order whole numbers

To order whole numbers, compare their digits by place value. Start with the greatest place—the hundred-thousands place for numbers up to 1,000,0001{,}000{,}000. If those digits are the same, compare the ten-thousands digits, then the thousands, and so on. The first different digit tells you which number is greater.

Example: Arrange these numbers from least to greatest:

407,215,470,125,399,999,407,251407{,}215,\quad 470{,}125,\quad 399{,}999,\quad 407{,}251

  1. Compare the hundred-thousands digits:

    • 407,215407{,}215 has 44
    • 470,125470{,}125 has 44
    • 399,999399{,}999 has 33
    • 407,251407{,}251 has 44

    Since 3<43<4, 399,999399{,}999 is the least number.

  2. Compare the three numbers that begin with 44. Their ten-thousands digits are:

    • 407,215407{,}215 has 00
    • 470,125470{,}125 has 77
    • 407,251407{,}251 has 00

    Since 0<70<7, 470,125470{,}125 is the greatest of these three.

  3. Compare 407,215407{,}215 and 407,251407{,}251. Their digits match through the hundreds place, so compare the tens digits:

    • 407,215407{,}215 has 11 ten
    • 407,251407{,}251 has 55 tens

    Since 1<51<5, 407,215<407,251407{,}215<407{,}251.

Therefore, from least to greatest:

399,999<407,215<407,251<470,125\boxed{399{,}999<407{,}215<407{,}251<470{,}125}

On a number line, the numbers farther to the left are less, and the numbers farther to the right are greater. To order from greatest to least, simply reverse the order.

Learn by doing: Order whole numbers

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    Number Sense - Ordering 3 Integers (ascending)

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