Question

Представь бесконечную периодическую десятичную дробь 0,2(64) в виде обыкновенной.

Answer 1

Решение задания на фото.

Answer 2

Converting the Infinite Periodic Decimal 0,2(64) to a Fraction

To convert the infinite periodic decimal 0,2(64) to a fraction, we can follow these steps:

Step 1: Let x = 0,2(64) Step 2: Multiply both sides of the equation by 10 to shift the decimal point to the right: 10x = 2,(64) Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part: 10x - x = 2,(64) - 0,2(64) Step 4: Simplify the equation: 9x = 2,(64) - 0,2(64) Step 5: Subtract the repeating part of the decimal: 9x = 2,64 - 0,264 Step 6: Simplify the equation: 9x = 2,375 Step 7: Divide both sides of the equation by 9 to solve for x: x = 2,375 / 9

Therefore, the infinite periodic decimal 0,2(64) can be represented as the fraction 2,375 / 9.