Expanded form means writing a number as a sum that shows the value of each digit, based on its place value. For example, 943 in expanded form is 900 + 40

Simple definition

  • Expanded form: a way of writing a number by “stretching it out” into the value of each digit.
  • You turn a compact (standard) number into an addition sentence that shows ones, tens, hundreds, etc.

Think of it like unpacking a suitcase: the number is the suitcase, and expanded form lays out everything that’s inside so you can see each part.

Basic examples

  • 254 → 200 + 50 + 4.
  • 77 → 70 + 7.
  • 4987 → 4000 + 900 + 80 + 7.

These all show clearly what each digit stands for (thousands, hundreds, tens, ones).

With decimals

You can also use expanded form with decimals to show tenths, hundredths, and so on.

  • 3.482 → 3 + 0.4 + 0.08 + 0.002.
  • 83.34 → 80 + 3 + 0.3 + 0.04.

This helps you see that:

  • The first digit after the decimal is tenths.
  • The next is hundredths.
  • The next is thousandths, etc.

Why teachers use expanded form

  • Builds number sense and place value understanding.
  • Makes it easier to add or subtract large numbers without a calculator.
  • Helps students see the difference between, for example, 304 and 340 (same digits, different place values).

Quick recap (TL;DR)

  • Expanded form = writing a number as a sum of each digit’s place value.
  • Whole number example: 834 = 800 + 30 + 4.
  • Decimal example: 3.482 = 3 + 0.4 + 0.08 + 0.002.

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