Base-Ten System Math Example 4

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

Example 4

easy
What is the value of 10010^0, 10110^1, 10210^2, and 10310^3?

Solution

  1. 1
    100=110^0 = 1 (any nonzero base to the zero power is 1).
  2. 2
    101=1010^1 = 10, 102=10010^2 = 100, 103=1,00010^3 = 1{,}000.

Answer

100=1,101=10,102=100,103=1,00010^0=1,\quad 10^1=10,\quad 10^2=100,\quad 10^3=1{,}000
The base-ten place values are consecutive powers of 10. Each step up multiplies by 10. The pattern continues in both directions: 10−1=0.110^{-1} = 0.1, 10−2=0.0110^{-2} = 0.01, etc. for decimal 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.

Learn more about Base-Ten System →

More Base-Ten System Examples

Example 1 easy

Express [formula] as a sum of powers of 10.

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 5 medium

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

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