1.285714 as a Fraction

Professor Greenline Explaining Math Concepts

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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. A fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 1.285714, we are going to learn how to convert a decimal to a fraction.

What is 1.285714 as a Fraction?

$1.285714 as a fraction$

Answer

The answer for 1.285714 as a fraction is 9/7.

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, any decimal number should be converted to a fraction for easy calculation. Here, 1.285714 is the number on the numerator and the base number 1 will be the denominator. Then, 1.285714 becomes 1.285714/1.

Step 2: To remove the decimal from a fraction, you need to identify if the decimal is repeating or not. The decimal 1.285714 is a repeating decimal. The repeating part is "285714", which has 6 digits.

Step 3: Let x = 1.285714285714... Multiply both sides by 10^6 (because the repeating section has 6 digits) to shift the decimal point: 1000000x = 1285714.285714...

Step 4: Subtract the original equation (x = 1.285714285714...) from this new equation: 1000000x - x = 1285714.285714... - 1.285714285714... This simplifies to: 999999x = 1285713 x = 1285713/999999

Step 5: Simplify the fraction. The GCD of 1285713 and 999999 is 142857. Divide both the numerator and denominator by their GCD: 1285713/999999 = 9/7

Thus, 1.285714 can be written as a fraction 9/7.