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Why is the digit 2 worth different amounts in 20 and 200?
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numerals and numeral systems
Examples of ancient symbols for the numbers 1 and 10.
The digit 2 represents different values in 20 and 200 because we use a positional numeral system. In this system, the value of a digit is determined by its specific position or place within the number.1
In the decimal positional numeral system, each position represents a power of 10. Consequently:
- In the number 20, the digit 2 is in the tens place, representing two tens (20).
- In the number 200, the digit 2 is in the hundreds place, representing two hundreds (200).1
This place value structure allows a limited set of symbols—0 through 9—to represent an infinite range of numbers by changing the significance of a digit based on where it is placed. Unlike many ancient systems that lacked this characteristic, modern positional systems make arithmetical calculations significantly more efficient.1