Which of the following multipliers will cause a number to be increased by 29.7%?

### Concept & Logic To increase a number by a certain percentage, you add that percentage of the number to the original number itself ($100\%$). The final multiplier is simply the decimal equivalent of the final percentage. $$ \text{Final Multiplier} = 1 + \frac{\text{Percentage Increase}}{100} $$ ### Step-by-Step Solution * Let the original number be $x$. The original number represents $100\%$ of itself, or $1 \cdot x$. * We want to increase this number by $29.7\%$. * The increase amount is $29.7\%$ of $x$, which can be written as $0.297x$. * The new number is the sum of the original number and the increase: $$ \text{New Number} = x + 0.297x $$ * Factor out $x$: $$ \text{New Number} = x(1 + 0.297) = 1.297x $$ * Therefore, the required multiplier is $1.297$. ### Exam Strategy & Shortcut A $29.7\%$ increase means the final value is $129.7\%$ of the original. To convert any percentage to a decimal multiplier, just divide by $100$ (move the decimal point two places to the left). $129.7 / 100 = 1.297$. ### Common Pitfall A very common mistake is confusing the percentage value with the decimal multiplier (e.g., choosing 129.7 or 12.97) by failing to divide by $100$ or moving the decimal point the wrong number of spaces. ### Final Answer **Therefore, the correct answer is 1.297.**