Question

算下列各题。

(2.dot{1}dot{2} div 0.dot{4} =)

Explanation:

⚡ Using what you learned: Repeating and Terminating Decimals

Step 1: Convert repeating decimals to fractions

Convert \( 2.\dot{1}\dot{2} \) to a fraction:

$$ 2.\dot{1}\dot{2} = 2 \frac{12}{99} = 2 \frac{4}{33} = \frac{70}{33} $$

Convert \( 0.\dot{4} \) to a fraction:

$$ 0.\dot{4} = \frac{4}{9} $$

Step 2: Divide the fractions

Set up the division and multiply by the reciprocal:

$$ \frac{70}{33} \div \frac{4}{9} = \frac{70}{33} \times \frac{9}{4} $$

Simplify the expression:

$$ \frac{70 \times 9}{33 \times 4} = \frac{70 \times 3}{11 \times 4} = \frac{35 \times 3}{11 \times 2} = \frac{105}{22} $$

Step 3: Convert back to a mixed number or repeating decimal

Convert \( \frac{105}{22} \) to a mixed number:

$$ \frac{105}{22} = 4 \frac{17}{22} $$

Convert \( \frac{17}{22} \) to a decimal:

$$ 17 \div 22 = 0.7727272... = 0.7\dot{7}\dot{2} $$

Thus:

$$ 4 \frac{17}{22} = 4.7\dot{7}\dot{2} $$

Answer:

$$ 4.7\dot{7}\dot{2} \text{ (or } 4\frac{17}{22}\text{)} $$