Base-Ten System Math Example 3

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Example 3

medium
Write 3,407 in expanded form using powers of 10.

Solution

  1. 1
    Identify each digit's place value: 3 is in the thousands place (10310^3), 4 is in the hundreds place (10210^2), 0 is in the tens place (10110^1), 7 is in the ones place (10010^0).
  2. 2
    Write each digit multiplied by its place value: 3ร—103+4ร—102+0ร—101+7ร—1003 \times 10^3 + 4 \times 10^2 + 0 \times 10^1 + 7 \times 10^0.
  3. 3
    Simplify: 3ร—1000+4ร—100+0ร—10+7ร—1=3000+400+0+7=3,4073 \times 1000 + 4 \times 100 + 0 \times 10 + 7 \times 1 = 3000 + 400 + 0 + 7 = 3{,}407 โœ“.

Answer

3,407=3ร—103+4ร—102+0ร—101+7ร—1003{,}407 = 3 \times 10^3 + 4 \times 10^2 + 0 \times 10^1 + 7 \times 10^0
Expanded form reveals how our number system works: each digit's value depends on its position. The digit 0 in the tens place is a placeholder โ€” it contributes nothing to the value but is essential for keeping other digits in the correct positions.

About Base-Ten System

The positional numeral system using ten as its base, where each digit's value depends on its position, with each place worth ten times the place to its right.

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