Question

3 3. Переведите периодическую десятичную дробь в обыкновенную: а) 0,(16),б) 3,201) и запишите решение.​

Answer 1

Ответ:

$a)0.(16) = \frac{16}{99} \\ \\ b)3.(201) = 3 \frac{201}{999} = 3 \frac{67}{333}$

Answer 2

Converting Periodic Decimal to Fraction

To convert the periodic decimal to a fraction: a) 0,(16)

The recurring decimal 0,(16) can be represented as 0.161616... where the 16 repeats infinitely. To convert this to a fraction, let x = 0.161616... Then, 100x = 16.161616... Subtracting the two equations: 100x - x = 16.161616... - 0.161616... 99x = 16 x = 16/99

Therefore, the fraction form of 0,(16) is 16/99.

b) 3.201

The decimal 3.201 is a non-recurring decimal. To convert it to a fraction, we can use the fact that 3.201 = 3 + 0.201. Let x = 0.201 Then, 1000x = 201.201... Subtracting the two equations: 1000x - x = 201.201... - 0.201... 999x = 201 x = 201/999

Therefore, the fraction form of 3.201 is 201/999.

So, the solutions are: a) 0,(16) = 16/99 b) 3.201 = 201/999