What percent of $7.2$ kg is $18$ gms?

### Concept & Formula When finding what percentage one quantity is of another, both quantities must be in the exact same unit of measurement. $$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Part = $18$ gms * Whole = $7.2$ kg * **Deduction:** * Convert the whole amount from kilograms (kg) to grams (gms) so the units match. * Since $1 \text{ kg} = 1000 \text{ gms}$, $7.2 \text{ kg} = 7.2 \times 1000 = 7200 \text{ gms}$. * **Calculation:** * Now apply the formula: * $\text{Percentage} = \left( \frac{18}{7200} \right) \times 100$ * Simplify by cancelling the zeros: * $\text{Percentage} = \frac{18}{72}$ * Divide numerator and denominator by $18$: * $\text{Percentage} = \frac{1}{4}$ * $\frac{1}{4} = 0.25\%$ ### Exam Strategy & Shortcut Once you convert the base to $7200$ gms, find $1\%$. $1\%$ of $7200 = 72$. The target is $18$, which is exactly one-fourth ($\frac{1}{4}$) of $72$. Therefore, the percentage is $\frac{1}{4}$ of $1\%$, which is $0.25\%$. ### Common Pitfall The most common mistake is ignoring the unit conversion and calculating $( \frac{18}{7.2} ) \times 100$, which incorrectly yields $250\%$. Always check that your units are identical before setting up the fraction. ### Final Answer **Therefore, the correct answer is .25%.**