मराठी

Mathematical Operation and Error Analysis

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Topics

Estimated time: 7 minutes
  • Scientific notation (exponential notation) 
  • Precision and accuracy of measurement
  • Significant Figures
  • Rules for deciding significant figures
  • Calculations with significant figures
Maharashtra State Board: Class 11

Definition: Percentage Error

The error expressed as a percentage of the true or measured value of a quantity, used to determine the accuracy of a measurement, is called the percentage error.

Maharashtra State Board: Class 11

Definition: Accuracy

The degree of closeness of a measured value to the true value, which increases as the error decreases, is called accuracy.

Maharashtra State Board: Class 11

Formula: Percentage Error in a

If the error in a is Δa, then:

Percentage error in a = \[\frac {Δa}{a}\] × 100

Maharashtra State Board: Class 11

Formula: Percentage Error in a^n

If the error in a is Δa, then:

Percentage error in an = ±n × \[\frac {Δa}{a}\] × 100

Maharashtra State Board: Class 11

Formula: Percentage error in ab

If the error in a is Δa and in b is Δb, then:

Percentage error in ab = \[\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)\times100\]

Maharashtra State Board: Class 11

Formula: Error in Division a/b

If the error in a is Δa and in b is Δb, then:

Percentage error in \[\frac {a}{b}\]= \[\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)\times100\]

Theorem: Accuracy

  • The smaller the error, the greater the accuracy.
  • For both product and division of two quantities, the percentage errors in the individual quantities are always added (never subtracted) to get the total percentage error.
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