Zero Math Example 4

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

Example 4

medium
The number 3,0203{,}020 has a zero in the tens place. How does removing that zero (writing 320 instead) change the number's value?

Solution

  1. 1
    3,020=3×103+0×102+2×101+0×100=3000+203{,}020 = 3 \times 10^3 + 0 \times 10^2 + 2 \times 10^1 + 0 \times 10^0 = 3000 + 20.
  2. 2
    320=3×102+2×101+0=300+20320 = 3 \times 10^2 + 2 \times 10^1 + 0 = 300 + 20.
  3. 3
    The values differ: 3,020−320=2,7003{,}020 - 320 = 2{,}700.

Answer

3,020≠320; removing the zero reduces the value by 2,7003{,}020 \neq 320 \text{; removing the zero reduces the value by } 2{,}700
The internal zero in 3,020 is a placeholder that positions the digit 3 in the thousands place. Removing it shifts 3 to the hundreds place, fundamentally changing the number. Zero as placeholder is not optional.

About Zero

The number representing the absence of quantity; the additive identity and placeholder in positional notation.

Learn more about Zero →

More Zero Examples

Example 1 easy

Evaluate: (a) [formula], (b) [formula], (c) [formula].

Example 2 medium

Why is [formula] undefined? Explain using the definition of division.

Example 3 easy

Is zero even or odd? Justify.

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