Calculer les incertitudes absolues à partir des incertitudes relatives et arrondir au premier chiffre significatif pour les valeurs suivantes: 200 (à 10%), 81% (à 10%), 427 (à 2%),... Calculer les incertitudes absolues à partir des incertitudes relatives et arrondir au premier chiffre significatif pour les valeurs suivantes: 200 (à 10%), 81% (à 10%), 427 (à 2%), 7241,21 (à 9 ppm).
Understand the Problem
La question demande de calculer l'incertitude absolue à partir de l'incertitude relative pour les valeurs données, et d'arrondir le résultat au premier chiffre significatif. Il faut donc calculer l'incertitude absolue pour chaque valeur (200, 81, 427, 7241.21) en utilisant le pourcentage ou la valeur en ppm fournie, puis arrondir le résultat au premier chiffre significatif.
Answer
20 8 9 0. 07
Answer for screen readers
20
8
9
- 07
Steps to Solve
- Calculate the absolute uncertainty for 200 with a 10% relative uncertainty
Absolute uncertainty = Value $\times$ Relative uncertainty
Absolute uncertainty $= 200 \times 10% = 200 \times 0.1 = 20$
- Calculate the absolute uncertainty for 81 with a 10% relative uncertainty
Note that the 81 already appears as a percentage. Absolute uncertainty $=$ Value $\times$ Relative uncertainty
Absolute uncertainty $= 81 \times 10% = 81 \times 0.1 = 8.1$
- Round the absolute uncertainty to the first significant digit
Round 8.1 to the first significant figure which is 8.
- Calculate the absolute uncertainty for 427 with a 2% relative uncertainty
Absolute uncertainty = Value $\times$ Relative uncertainty
Absolute uncertainty $= 427 \times 2% = 427 \times 0.02 = 8.54$
- Round the absolute uncertainty to the first significant digit
Round 8.54 to the first significant figure which is 9.
- Calculate the absolute uncertainty for 7241.21 with a 9 ppm relative uncertainty
ppm means "parts per million", so 9 ppm means 9 parts out of 1,000,000. Absolute uncertainty = Value $\times$ Relative uncertainty
Absolute uncertainty $= 7241.21 \times \frac{9}{1000000} = 7241.21 \times 0.000009 = 0.06517089$
- Round the absolute uncertainty to the first significant digit
Round 0.06517089 to the first significant figure which is 0.07.
20
8
9
- 07
More Information
"ppm" means "parts per million", which is a way of expressing very small concentrations.
Tips
A common mistake is not rounding to the first significant figure. Another common mistake is forgetting to convert percentages into decimals before multiplying. Also, its important to understand what ppm stands for.
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