Place-value weighting — “Each position in a multi-digit decimal number has a weight equal to a power of 10 only.” Evaluate the claim.
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
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ACorrect
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BIncorrect
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COnly true for integers, not fractions
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DOnly true for scientific notation
Answer
Correct Answer: Correct
Explanation
Introduction / Context: In positional number systems, each digit slot carries a weight equal to a power of the base. For the decimal system, the base is ten. This question tests whether you remember that decimal place values are powers of 10 for both integer and fractional parts.Given Data / Assumptions:
- Base (radix) for decimal = 10.
- Weights to the left of the point: 10^0, 10^1, 10^2, …
- Weights to the right: 10^-1, 10^-2, 10^-3, …
Concept / Approach: The value of a number is sum(digit_i * base^i). In decimal, base = 10, so the weights are exclusively powers of 10. This holds for signed numbers, integers, and fixed/floating formats; sign and scaling do not change the underlying positional weights.Step-by-Step Solution:
Write a decimal like 347.52.Assign weights: 310^2 + 410^1 + 710^0 + 510^-1 + 2*10^-2.Observe all exponents are powers of 10; no other bases appear.Verification / Alternative check:
Compare with binary place values: powers of 2; with hex: powers of 16. Principle is consistent across bases.Why Other Options Are Wrong:
Incorrect: Would deny the definition of positional notation.Only true for integers: Fractional places are also powers of 10 with negative exponents.Only true for scientific notation: Scientific notation is a scaled decimal; positional weights remain powers of 10.Common Pitfalls:
Confusing digit value with its place value weight.Mistaking percent or per-unit notation as different bases; they are decimals with scaling.Final Answer:
Correct