Base-Ten System Math Example 2

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Example 2

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

Solution

  1. 1
    In base ten, each position is worth 10 times the position to its right.
  2. 2
    Multiplying by 10 shifts every digit one place to the left: the ones digit moves to tens, tens to hundreds, etc.
  3. 3
    The ones place becomes empty, so a zero is written as a placeholder: e.g., 47Ɨ10=47047 \times 10 = 470.

Answer

47Ɨ10=470Ā (eachĀ digitĀ shiftsĀ oneĀ placeĀ left;Ā onesĀ becomeĀ aĀ zeroĀ placeholder)47 \times 10 = 470 \text{ (each digit shifts one place left; ones become a zero placeholder)}
Multiplying by 10 in base ten is equivalent to shifting all digits one position to the left. The vacated ones position must be filled with 0. This is a structural consequence of positional notation, not a coincidence.

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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