Problem — Significant figures, ranking

Problem

Four measurements of the same length: (A) $1$ cm; (B) $1{,}2$ cm; (C) $1{,}23$ cm; (D) $1{,}234$ cm. Rank them from least precise to most precise, stating the number of significant figures for each.

Solution

The number of significant figures counts the digits known with certainty plus the first uncertain digit: the more significant figures a measurement has, the finer the instrument’s resolution and the smaller the relative uncertainty.

Let’s count the significant figures:

• A $= 1$ cm → 1 significant figure;
• B $= 1{,}2$ cm → 2 significant figures;
• C $= 1{,}23$ cm → 3 significant figures;
• D $= 1{,}234$ cm → 4 significant figures.

Since more significant figures correspond to a more precise measurement, the increasing order of precision (from least precise to most precise) follows the increasing order of the number of digits: $A\ (1) \;<\; B\ (2) \;<\; C\ (3) \;<\; D\ (4)$

$\ev{A < B < C < D \quad (\text{from 1 to 4 significant figures})}$

Links

Topics: Metodo sperimentale Concepts: Cifre significative e incertezza Skills: Ragionamento di ranking