Decimal system digits — fact check: Evaluate the statement: “The decimal number system consists of the digits 0–10.”

Introduction / Context:Decimal (base-10) is the everyday numbering system. Precision in terminology—especially which symbols are valid digits—is important when explaining positional notation and performing base conversions.

Given Data / Assumptions:

• Base-10 requires exactly ten unique digit symbols.
• Their symbols determine which characters may appear in a valid decimal numeral.
• We are discussing symbols, not numeric values.

Concept / Approach:The decimal system uses ten symbols: 0,1,2,3,4,5,6,7,8,9. The number “10” is not a single digit; it is a two-digit numeral composed of the digits “1” and “0.” Thus, saying “digits 0–10” is incorrect because it treats “10” as a digit symbol rather than a numeral value.

Step-by-Step Solution:List the valid digit symbols: 0 through 9 (ten symbols total).Explain that “10” requires positional notation (1×10^1 + 0×10^0) and therefore two digits.Conclude the claim is false as stated.Reinforce: this mirrors how hex uses 16 symbols (0–9, A–F), not “0–15.”

Verification / Alternative check:Any textbook on number systems or arithmetic defines decimal digits as 0–9; calculators and numeric parsers accept only these characters for decimal input.

Why Other Options Are Wrong:Including “10” as a digit confuses numerals with digits; floating-point formats do not change digit symbol sets.

Common Pitfalls:Equating the count of digits (ten) with the largest digit value (9); misusing hyphen ranges like “0–10” when “0–9” is intended.

Final Answer:Incorrect (digits are 0–9)