Question

Перевести периодическую дробь в обыкновенную десятичную дробь 4,4(3)

Answer 1

(443 - 44)/90 = 399/90 = 133/30 

Answer 2

Converting a Periodic Fraction to a Decimal Fraction

To convert the periodic fraction 4.4(3) to an ordinary decimal fraction, we can use the following method:

Let x = 4.4(3)

Multiply x by 10 to move the decimal point one place to the right: 4.4(3) * 10 = 44.(3)

Subtract the original equation from the new equation to eliminate the repeating decimal: 10x - x = 44.(3) - 4.4(3) 9x = 40 x = 40 / 9

Now, let's calculate the result.

Calculation: 10x - x = 44.(3) - 4.4(3) 9x = 40 x = 40 / 9

So, the ordinary decimal fraction equivalent of 4.4(3) is 40 / 9.

Explanation:

The process of converting a periodic fraction to an ordinary decimal fraction involves multiplying the fraction by an appropriate power of 10 to shift the decimal point and then subtracting the original equation from the new equation to eliminate the repeating decimal. This results in an equation that can be solved to find the equivalent ordinary decimal fraction.

I hope this helps! If you have further questions, feel free to ask.