1.42857142857 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. Fraction is one of its kind. It is always represented in the form of p/q, where p is the numerator and q is the denominator. 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, 0.375. We are going to learn how to convert a decimal to a fraction.

1.42857142857 as a Fraction for US Students

What is 1.42857142857 as a Fraction?

$1.42857142857 as a fraction$ Answer

The answer for 1.42857142857 as a fraction will be 10/7.

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: Recognize that 1.42857142857 is a repeating decimal. The repeating part is 428571, which repeats indefinitely.

Step 2: Let x = 1.42857142857. To eliminate the repeating decimal, multiply x by 10^6 (since 428571 has six digits), obtaining 1000000x = 1428571.428571...

Step 3: Subtract the original x from this equation: 1000000x - x = 1428571.428571... - 1.428571... 999999x = 1428570

Step 4: Solve for x: x = 1428570 / 999999

Step 5: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 142857: x = (1428570 ÷ 142857) / (999999 ÷ 142857) = 10/7

Thus, 1.42857142857 can be written as a fraction 10/7.

Important Glossaries for 1.42857142857 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
Repeating Decimal: A decimal fraction that has a repeating sequence of digits indefinitely.
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.
Greatest Common Divisor (GCD): The largest positive integer that divides the numbers without a remainder.