Base-Ten System Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumWhy does multiplying any whole number by 10 append a zero? Explain using the base-ten structure.
Solution
- 1 In base ten, each position is worth 10 times the position to its right.
- 2 Multiplying by 10 shifts every digit one place to the left: the ones digit moves to tens, tens to hundreds, etc.
- 3 The ones place becomes empty, so a zero is written as a placeholder: e.g., .
Answer
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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