Base-Ten System Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Express 5,3045{,}304 as a sum of powers of 10.

Solution

  1. 1
    Identify each digit: 55 (thousands), 33 (hundreds), 00 (tens), 44 (ones).
  2. 2
    Write each as a power of 10: 5×103+3×102+0×101+4×1005 \times 10^3 + 3 \times 10^2 + 0 \times 10^1 + 4 \times 10^0.
  3. 3
    Verify: 5000+300+0+4=5,3045000 + 300 + 0 + 4 = 5{,}304.

Answer

5×103+3×102+4×1005 \times 10^3 + 3 \times 10^2 + 4 \times 10^0
The base-ten system assigns each position a power of 10: ones (10010^0), tens (10110^1), hundreds (10210^2), thousands (10310^3), etc. Writing a number in this form makes its structure explicit and connects place value to exponents.

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.

Learn more about Base-Ten System →

More Base-Ten System Examples

Example 2 medium

Why does multiplying any whole number by 10 append a zero? Explain using the base-ten structure.

Example 3 medium

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

Example 4 easy

What is the value of [formula], [formula], [formula], and [formula]?

Example 5 medium

A number [formula]. What is [formula]?

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