Convert the following repeating decimal to a fraction in simplest form.
point, 4, start overline, 3, end overline
To convert the repeating decimal 0.43ˈ to a fraction, we follow these steps:
Let x = 0.43ˈ
Multiplying both sides of the equation by 100 (to move the decimal point two places to the right) gives us:
100x = 43.43ˈ
We subtract the original equation from the multiplied equation to eliminate the repeating decimal part:
100x - x = 43.43ˈ - 0.43ˈ
99x = 43
To isolate x (the repeating decimal), we divide both sides of the equation by 99:
x = 43/99
Therefore, the repeating decimal 0.43ˈ can be converted to the fraction 43/99 in simplest form.