0.71428571428 as a fraction in simplest form

0.71428571428 as a fraction in simplest form

The Correct Answer and Explanation is:

Answer:
0.71428571428 as a fraction in simplest form is 5/7.

---

Explanation

To convert the decimal 0.71428571428 to a fraction, we first notice that the number is repeating. If we round it or truncate it slightly, we get:

0.714285714285… which repeats the digits 714285.

This kind of decimal is called a repeating decimal. The repeating part here is 714285, which has 6 digits.

We can use algebra to convert it into a fraction.

Let:

x = 0.714285714285…

Since the repeating block is 6 digits long, we multiply both sides by 1,000,000 to shift the decimal point 6 places:

1,000,000x = 714285.714285…

Now subtract the original x:

1,000,000x – x = 714285.714285… – 0.714285…

This simplifies to:

999,999x = 714285

Now solve for x:

x = 714285 / 999999

We can now simplify this fraction.

Let’s divide both numerator and denominator by their greatest common divisor (GCD). The GCD of 714285 and 999999 is 142857.

So: 714285999999=714285÷142857999999÷142857=57\frac{714285}{999999} = \frac{714285 ÷ 142857}{999999 ÷ 142857} = \frac{5}{7}

Thus, 0.71428571428 is approximately 5/7 in fractional form.

Even though the decimal provided was cut off (ending in …428), it clearly imitates the repeating decimal 0.714285…, which is the repeating representation of 5/7.

This form is simplest because 5 and 7 have no common factors other than 1.

So, the fraction 5/7 is the correct and simplified representation of 0.71428571428.