0.714285714 as a Fraction

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

Numbers can be categorized into different types. A fraction is one of its kinds. It is always represented in the form of p/q, where p is the numerator and q is the denominator. Fractions represent a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2; numbers in decimal are expressed with a decimal point (.), such as 0.714285714. We are going to learn how to convert a decimal to a fraction.

What is 0.714285714 as a Fraction?

$0.714285714 as a fraction$

Answer

The answer for 0.714285714 as a fraction is 5/7.

Explanation

Converting a decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Firstly, recognize that 0.714285714 is a repeating decimal. Identify the repeating part, which is 714285.

Step 2: Let x = 0.714285714... Then, multiply both sides by 10^6 (since there are 6 repeating digits) to shift the decimal point to the right: 1,000,000x = 714285.714285...

Step 3: Subtract the original equation (x = 0.714285714...) from this new equation: 1,000,000x - x = 714285.714285... - 0.714285714... 999,999x = 714285

Step 4: Solve for x by dividing both sides by 999,999: x = 714285/999999

Step 5: Simplify the fraction by finding the greatest common divisor (GCD) of 714285 and 999999, which is 142857. Divide both the numerator and the denominator by 142857: 714285/999999 = 5/7

Thus, 0.714285714 can be written as a fraction 5/7.

Important Glossaries for 0.714285714 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.
Repeating Decimal: A decimal in which a digit or group of digits repeats infinitely.
Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.
Denominator: The bottom part of a fraction, showing how many parts make up a whole.