Anand has drawn an angle of measure $45^{\circ} 27'$ when he was asked to draw an angle of $45^{\circ}$. The percentage error in his drawing is

### Concept & Formula This problem requires converting angular minutes into degrees to establish a uniform unit of measurement before calculating the standard percentage error. Remember that $1^{\circ} = 60'$ (minutes). $$\text{Percentage Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100$$ ### Step-by-Step Solution **Given:** * True angle required = $45^{\circ}$ * Measured (drawn) angle = $45^{\circ} 27'$ **Calculation:** * Calculate the absolute error in the drawing: $$\text{Error} = 45^{\circ} 27' - 45^{\circ} = 27'$$ * Convert the error from minutes into degrees. Since $60' = 1^{\circ}$: $$\text{Error in degrees} = \frac{27}{60}^{\circ}$$ * Simplify the fraction by dividing numerator and denominator by $3$: $$\text{Error in degrees} = \frac{9}{20}^{\circ} = 0.45^{\circ}$$ * Apply the percentage error formula: $$\text{Percentage Error} = \left( \frac{0.45}{45} \right) \times 100$$ * Calculate the final percentage: $$\text{Percentage Error} = \left( \frac{45}{45 \times 100} \right) \times 100 = 1\%$$ ### Exam Strategy & Shortcut Keep the error as a fraction to make cancellation obvious. The error is $\frac{27}{60}$ of a degree. The base is $45$ degrees. Percentage = $\frac{(\frac{27}{60})}{45} \times 100$ Rearrange the terms: $\frac{27}{60 \times 45} \times 100$ Cancel $100$ and $60$ (divide by $20$): $\frac{27 \times 5}{3 \times 45}$ $27 \times 5 = 135$, and $3 \times 45 = 135$. $\frac{135}{135} = 1.0$. ### Common Pitfall A common error is treating the minutes as a direct decimal (i.e., treating $45^{\circ} 27'$ as $45.27^{\circ}$). This leads to an incorrect absolute error of $0.27$, which yields a percentage error of $0.6\%$, leading to confusion when the option isn't there or a wild guess. ### Final Answer **Therefore, the correct answer is 1.0.**