1 m of an object is to be represented by 10 cm on the drawing scale. The representative fraction (R.F.) of the scale is

### Concept & Formula This question tests the fundamental concept of Map Scaling and Representative Fraction (R.F.). The Representative Fraction is the ratio of the distance on the drawing (or map) to the actual distance on the ground. The critical rule is that **both quantities must be in the same units** before simplifying the fraction. $$ R.F. = \frac{\text{Distance on Drawing}}{\text{Actual Distance}} $$ ### Step-by-Step Solution * **Given:** Distance on drawing = $10 \text{ cm}$ Actual distance = $1 \text{ m}$ * **Calculation:** Convert the actual distance into the same units as the drawing scale (centimeters): $$ 1 \text{ m} = 100 \text{ cm} $$ * Apply the R.F. formula: $$ R.F. = \frac{10 \text{ cm}}{100 \text{ cm}} $$ * Simplify the fraction by dividing numerator and denominator by 10: $$ R.F. = \frac{1}{10} $$ ### Exam Strategy & Shortcut For linear scale questions, strictly focus on unit conversion. Memorize the metric ladder: $1 \text{ m} = 100 \text{ cm}$. Plug the numbers in as $\frac{\text{Small Value}}{\text{Large Value}}$ (since maps shrink reality) and ensure units match: $\frac{10}{100} = \frac{1}{10}$. This should take less than 10 seconds. ### Common Pitfall The single most common mistake is ignoring unit conversion and directly dividing the given numbers, leading to an R.F. of $\frac{10}{1} = 10$, or writing it blindly as $\frac{1}{100}$ because they see "$1 \text{ m}$". Always harmonize the units first. ### Final Answer Therefore, the correct answer is **$\frac{1}{10}$**.