One hundredth of centimetre when written in fractions of kilometres, is equal to

### Concept & Formula This is a unit conversion problem. You must bridge the gap between centimeters and kilometers using meters as the intermediary step, utilizing the standard metric scale. $$1 \text{ km} = 1000 \text{ m}$$ $$1 \text{ m} = 100 \text{ cm}$$ $$\Rightarrow 1 \text{ km} = 100,000 \text{ cm} = 10^5 \text{ cm}$$ ### Step-by-step Solution **Given:** We need to convert "one hundredth of a centimetre" to kilometres. One hundredth of a cm = $\frac{1}{100}$ cm = $10^{-2}$ cm. **Calculation:** Since $1 \text{ km} = 10^5 \text{ cm}$, the conversion factor from cm to km is dividing by $10^5$ (or multiplying by $10^{-5}$). Convert the value: $$10^{-2} \text{ cm} \times 10^{-5} \text{ km/cm} = 10^{-7} \text{ km}$$ Expand the exponential notation to a decimal fraction: $10^{-7}$ means the decimal point moves 7 places to the left, resulting in 6 zeros after the decimal point before the 1. $$10^{-7} = 0.0000001$$ ### Exam Strategy & Shortcut Track the zeros logically: $2$ zeros to get from cm to m, $3$ zeros to get from m to km, and $2$ zeros for "one hundredth". Add them up: $2 + 3 + 2 = 7$ zeros of shift. The correct answer must have the 1 at the 7th decimal place ($6$ visual zeros after the dot). ### Common Pitfall Losing track of the decimal zeroes. Students often forget to count the original fraction ("one hundredth") and just calculate $1 \text{ cm}$ to km ($10^{-5}$), selecting option (b) by mistake. ### Final Answer Therefore, the correct answer is $0.0000001$.