Expanded form expresses a number as the sum of each digit multiplied by its place value. For example, 4,523 = 4,000 + 500 + 20 + 3 = (4 × 1000) + (5 × 100) + (2 × 10) + (3 × 1). It reinforces understanding of the base-10 number system.
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Pro Tip
Expanded form is the foundation of the standard multiplication algorithm. 23 × 45 = (20+3) × (40+5) = 800 + 100 + 120 + 15 = 1,035.
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Did You Know?
The base-10 number system (decimal) likely developed because humans have 10 fingers. The Babylonians used base-60 (for time and angles), the Mayans used base-20, and computers use base-2 (binary).
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