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Expanded Form Worksheets

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Write numbers to 1,000,000 in expanded form and back to standard form, with parts out of order, missing parts and expanded form with multiplication.

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Expanded form

Write numbers to 1,000,000 in expanded form, back in standard form, with parts out of order, with a missing part and with multiplication.

Print at 100% (actual size) for the cleanest tracing lines.

About these expanded form worksheets

Expanded form writes a number as the sum of the values of its digits. 47,302 in expanded form is 40,000 + 7,000 + 300 + 2. Each part is one digit times its place value, and a 0 digit adds nothing, so it has no part. Written with multiplication, the same number is (4 × 10,000) + (7 × 1,000) + (3 × 100) + (2 × 1).

Expanded form is how children prove they understand place value: that the 4 in 47,302 means 40,000, not 4. It also prepares them for multi-digit multiplication and division, where every method splits numbers into these same parts.

These pages go both ways. Children write numbers in expanded form, put expanded form back into standard form (including parts listed out of order, which forces them to think about each place), find a missing part, and write expanded form with multiplication. Numbers run up to six digits, the 4th grade range.

Standards

  • CCSS.MATH.CONTENT.4.NBT.A.2Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
  • CCSS.MATH.CONTENT.4.NBT.A.1Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

How to use them

  1. Start with Write in Expanded Form, saying each digit's value out loud.
  2. Use Expanded Form to Standard Form next, then the out-of-order page.
  3. Give the missing-part page as a check: it only works if the child knows what each part is worth.
  4. Use expanded form with multiplication last, as a bridge to 5th grade.

Teaching tips

  • A 0 digit has no part in expanded form: 5,040 = 5,000 + 40.
  • When the parts are out of order, sort them from biggest to smallest first.
  • Count the zeros in each part: 300 has two, so its digit goes in the hundreds place.
  • A place value chart makes the link clear.

Questions teachers and parents ask

What is expanded form?

Expanded form writes a number as the sum of the values of its digits. 3,482 is 3,000 + 400 + 80 + 2.

What happens to zeros in expanded form?

A digit that is 0 has a value of 0, so it is left out. 6,045 is 6,000 + 40 + 5.

What is expanded form with multiplication?

Each part is written as a digit times its place value: 3,482 = (3 × 1,000) + (4 × 100) + (8 × 10) + (2 × 1).