Question

Представьте бесконечную десятичную периодическую 0,4(3) в виде обыкновенной​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Converting the Infinite Decimal 0.4(3) to a Fraction

To convert the infinite decimal 0.4(3) to a fraction, we can use algebraic techniques. Let's denote the repeating part of the decimal as 'x'.

We can multiply both sides of the equation by a power of 10 to shift the decimal point to the right. Since there is one digit repeating after the decimal point, we can multiply by 10.

So, 10x = 4.3333...

Next, we subtract the original equation from the multiplied equation to eliminate the repeating part:

10x - x = 4.3333... - 0.4(3)

Simplifying this equation gives us:

9x = 3.9333...

Now, we can solve for 'x' by dividing both sides of the equation by 9:

9x/9 = 3.9333.../9

x = 0.437037...

Therefore, the fraction equivalent of the infinite decimal 0.4(3) is 437/999.

Please note that this is an approximate fraction, as the decimal 0.4(3) is a repeating decimal and cannot be expressed exactly as a fraction.