Skill: Write whole numbers in expanded form

Explanation and Free Practice Resources

A whole number can be decomposed into the sum of the values represented by its digits in each place—for example, 52,406 = 50,000 + 2,000 + 400 + 6. This representation makes the base-ten structure and the role of zero as a placeholder explicit, supporting accurate comparison, computation, and later work with larger numbers; the scope is limited to whole numbers through 100,000, not decimal or more generalized expanded notation.

Detailed Explanation: Write whole numbers in expanded form

To write a whole number in expanded form, break it apart by place value. Write the value of each digit, then add the values together.

Example: Write (63,042)(63{,}042) in expanded form.

  1. Identify the value of each digit:

    • 66 is in the ten-thousands place: (60,000)(60{,}000)
    • 33 is in the thousands place: (3,000)(3{,}000)
    • 00 is in the hundreds place: 00
    • 44 is in the tens place: (40)(40)
    • 22 is in the ones place: 22
  2. Add the place values:

63,042=60,000+3,000+0+40+263{,}042=60{,}000+3{,}000+0+40+2

Since adding 00 does not change the number, the expanded form is usually written as:

63,042=60,000+3,000+40+2\boxed{63{,}042=60{,}000+3{,}000+40+2}

The 00 is a placeholder showing that there are no hundreds.

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Place Value - Normal to Expanded Form (Numbers)


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