Convert 0.031\overline{4}$ to a fraction in simplest form.

Answer 1

To convert the repeating decimal 0.031\overline{4} to a fraction, we can use the following steps:

Let x = 0.031\overline{4}

Multiply both sides by 1000 to move the decimal point:

1000x = 31.4444...

Subtract the original equation from the new equation to eliminate the repeating decimal:

1000x - x = 31.4444... - 0.0314
999x = 31.413
x = 31.413 / 999

To simplify the fraction, we can divide both the numerator and the denominator by 3:

31.413 / 999 = 31.413 ÷ 3 / 999 ÷ 3
x = 10.471 / 333

Therefore, 0.031\overline{4}$ is equal to \boxed{\frac{10.471}{333}}$.

Answer 2

bad form to include decimals in a fraction
since 0.4444... = 4/9
0.0004444... = 4/9000
so
0.031444... = 31/1000 + 4/9000 = 283/9000

Answer 3

You are correct, I apologize for the mistake in including decimals in the fraction.

0.031\overline{4} can be written as 31/1000 + 4/9000, which simplifies to 283/9000.

Therefore, 0.031\overline{4}$ is equal to \boxed{\frac{283}{9000}}$. Thank you for pointing out the error.