Base-Ten System Math Example 5

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

Example 5

medium
A number N=3×104+7×102+5×100N = 3 \times 10^4 + 7 \times 10^2 + 5 \times 10^0. What is NN?

Solution

  1. 1
    3×104=30,0003 \times 10^4 = 30{,}000. 7×102=7007 \times 10^2 = 700. 5×100=55 \times 10^0 = 5.
  2. 2
    N=30,000+700+5=30,705N = 30{,}000 + 700 + 5 = 30{,}705.

Answer

30,70530{,}705
Assembling a number from its power-of-10 components requires careful placement. Missing powers (here 10310^3 and 10110^1) contribute zero and produce placeholder zeros in those 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 4 easy

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

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