Order large whole numbers

Ordering large whole numbers depends on the base-ten place-value structure: compare the number of digits first, then compare digits from the greatest place value to the right until the first difference determines which quantity is greater. This understanding supports accurate use of $<$ , $>$ , and $=$ , ordering in ascending or descending sequence, and interpreting standard, expanded, and number-line representations; negative integers, decimals, and scientific notation are outside this scope.

Detailed Explanation: Order large whole numbers

To order large whole numbers, compare them from left to right:

Count the digits. A number with more digits is greater.
If the numbers have the same number of digits, compare the digits in the greatest place value first.
Continue to the right until you find the first different digit. The number with the greater digit is greater.

Example: Order these numbers from least to greatest:

582{,}104,\quad 58{,}920,\quad 582{,}014,\quad 600{,}003

First, count the digits:

$(58{,}920)$ has $5$ digits.
The other numbers have $6$ digits.

Therefore, $(58{,}920)$ is the least number.

Now compare the three $6$ -digit numbers. Look at the hundred-thousands place:

$(582{,}104)$ has $5$ .
$(582{,}014)$ has $5$ .
$(600{,}003)$ has $6$ .

Since $6$ is greater than $5$ , $(600{,}003)$ is the greatest number.

Compare $(582{,}104)$ and $(582{,}014)$ . Their digits match through the thousands place. At the hundreds place:

$(582{,}104)$ has $1$ .
$(582{,}014)$ has $0$ .

Because $(1>0)$ , $(582{,}104)$ is greater than $(582{,}014)$ .

So, from least to greatest:

\boxed{58{,}920<582{,}014<582{,}104<600{,}003}

For greatest to least, reverse the order.

Learn by doing: Order large whole numbers

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Number Sense - Ordering 3 Integers (ascending)

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Order large whole numbers

Detailed Explanation: Order large whole numbers

Learn by doing: Order large whole numbers

Practice with unlimited practice problems

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Number Sense - Ordering 3 Integers (ascending)