1. **Convert 0.14 to a fraction and match options** 0.14 as a fraction is $$ \frac{14}{100} = \frac{7}{50} $$ which does not exactly match any option. Let's check each option by decimal conversion: (a) $$ \frac{11}{90} \approx 0.1222 $$ (b) $$ \frac{13}{90} \approx 0.1444 $$ (c) $$ \frac{17}{99} \approx 0.1717 $$ (d) $$ \frac{19}{9} \approx 2.1111 $$ Closest is (b) 13/90 for 0.14 but slightly off; likely (b) is intended. 2. **Convert 0.752 to a fraction and match options** Try representing 0.752 as a fraction with denominator close to options: Option (a) $$ \frac{677}{990} \approx 0.6838 $$ Option (b) $$ \frac{677}{900} \approx 0.7522 $$ Option (c) $$ \frac{752}{900} = \frac{376}{450} = \frac{188}{225} \approx 0.8377 $$ Option (d) $$ \frac{752}{999} \approx 0.75275 $$ Closest decimal to 0.752 is (b) 677/900 or (d) 752/999. (b) = 0.7522 is very close. 3. **Convert 5.27 to fraction and select option** Change 5.27 to an improper fraction to check options: Multiply fractional parts: decimals are with denominator 100, so $$ 5.27 = \frac{527}{100} $$ Options: (a) $$ \frac{57}{11} \approx 5.1818 $$ (b) $$ \frac{58}{11} \approx 5.2727 $$ (c) $$ \frac{59}{11} \approx 5.3636 $$ (d) $$ \frac{60}{11} \approx 5.4545 $$ Closest match is (b) $$ \frac{58}{11} $$. 4. **Find n such that 83216.5 = 8.32165 \times 10^n** Move decimal from 83216.5 to 8.32165: Since $$8.32165 \times 10^4 = 83216.5 $$ So, $$ n = 4 $$ Answers (a) or (b) show 4, so n = 4. 5. **Find smallest multiplier for 1575 to be a perfect square** Prime factorize 1575: $$ 1575 = 3^2 \times 5^2 \times 7 $$ To make it perfect square, multiply by $$7$$ to make $$7^2$$: Smallest number = 7. **Final answers:** 1. (b) 13/90 2. (b) 677/900 3. (b) 58/11 4. (a) 4 5. 7 (not from options but mathematical answer)