If $2994 \div 14.5 = 172$, then $29.94 \div 1.45 = x$

### Concept & Strategy When adjusting both the dividend and the divisor by decimal shifts, the overall quotient shifts by the net difference in decimal places. ### Step-by-Step Solution * The given equation can be written as: $$ \frac{2994}{14.5} = 172 $$ * We need to find the value of: $$ \frac{29.94}{1.45} $$ * Convert the target decimals using powers of $10$: $$ \frac{2994 \times 10^{-2}}{145 \times 10^{-2}} $$ Wait, the original denominator is $14.5$. Let us adjust the target fraction to match the known format: $$ \frac{29.94}{1.45} = \frac{29.94 \times 100}{1.45 \times 10} \times \frac{1}{10} $$ $$ = \frac{2994}{14.5} \times \frac{1}{10} $$ * Substitute the known value ($172$): $$ 172 \times \frac{1}{10} = 17.2 $$ ### Exam Strategy & Shortcut Compare the new numbers to the old numbers. The dividend ($2994$) becomes smaller by a factor of $100$. The divisor ($14.5$) becomes smaller by a factor of $10$. The net change to the quotient is division by $10$ ($100 \div 10 = 10$). Thus, $172 \div 10 = 17.2$. ### Common Pitfall Students often apply the $100$ shift and the $10$ shift in the wrong direction, mistakenly arriving at $1.72$ or $1720$. Remember that decreasing the dividend decreases the result, but decreasing the divisor increases the result. ### Final Answer **Therefore, the correct answer is $17.2$.**