Question

Запишите 1,2(34) в виде обыкновенной дроби. Как можно подробнее, пожалуйста.

Answer 1

Х=1,23434
10х=12,3434
1000х=1234,3434
1000х-10х=1234,3434-12,3434
990х=1222
х=1222/990

Answer 2

Converting 1,2(34) to a Fraction

To convert the number 1,2(34) to a fraction, we need to understand the notation used. The number 1,2(34) represents a repeating decimal, where the digits 34 repeat indefinitely.

To convert this repeating decimal to a fraction, we can follow these steps:

Step 1: Let x be the repeating decimal 1,2(34). Step 2: Multiply x by a power of 10 to eliminate the repeating part. Since there are two digits in the repeating part (34), we multiply x by 100. Step 3: Subtract x from the result obtained in step 2 to eliminate the repeating part. Step 4: Solve the resulting equation to find the value of x. Step 5: Express the value of x as a fraction.

Let's go through these steps in detail:

Step 1: Let x = 1,2(34).

Step 2: Multiply x by 100 to eliminate the repeating part: 100x = 134,34(34).

Step 3: Subtract x from 100x: 100x - x = 134,34(34) - 1,2(34).

Simplifying the equation: 99x = 133.

Step 4: Solve for x: x = 133/99.

Step 5: Express x as a fraction: x = 1 34/99.

Therefore, the number 1,2(34) can be written as the fraction 1 34/99.

Please note that the above steps are based on mathematical principles and do not specifically cite any external sources.