Question

1. $8.17 \times 2.34 =$
2. $53.48 \div 0.27 =$
3. $9.58 \div 5.127 =$
4. $87.90 \times 0.0092 =$

Explanation:

Step1: Convert repeating decimals to fractions

For $2.\dot{3}\dot{4}$: Let $x=2.\dot{3}\dot{4}$, then $100x=234.\dot{3}\dot{4}$. Subtract: $100x-x=234-2$, so $99x=232$, $x=\frac{232}{99}$.
Calculate $8.17\times\frac{232}{99}$: $8.17=\frac{817}{100}$, so $\frac{817}{100}\times\frac{232}{99}=\frac{817\times232}{9900}=\frac{189544}{9900}\approx19.15$

Step2: Convert repeating decimal to fraction

For $0.\dot{2}\dot{7}$: Let $y=0.\dot{2}\dot{7}$, then $100y=27.\dot{2}\dot{7}$. Subtract: $100y-y=27$, so $99y=27$, $y=\frac{27}{99}=\frac{3}{11}$.
Calculate $53.48\div\frac{3}{11}$: $53.48=\frac{1337}{25}$, so $\frac{1337}{25}\times\frac{11}{3}=\frac{14707}{75}\approx196.09$

Step3: Direct decimal division

$9.58\div5.127=\frac{9.58}{5.127}\approx1.87$

Step4: Direct decimal multiplication

$87.90\times0.0092=87.9\times0.0092$
Calculate $87.9\times0.0092=0.80868$

Answer:

1. $\approx19.15$
2. $\approx196.09$
3. $\approx1.87$
4. $0.80868$