0.428571428571 as a Fraction

Professor Greenline Explaining Math Concepts

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Numbers can be categorized into different types. 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, 0.428571428571. We are going to learn how to convert a repeating decimal to a fraction.

What is 0.428571428571 as a Fraction?

$0.428571428571 as a fraction$

Answer

The answer for 0.428571428571 as a fraction will be 3/7.

Explanation

Converting a repeating decimal to a fraction involves a few additional steps compared to converting a terminating decimal. Follow the steps below to find the answer.

Step 1: Let x equal the repeating decimal: x = 0.428571428571...

Step 2: Multiply x by 10^6 (since the repeating block "428571" has 6 digits) to shift the decimal point: 1000000x = 428571.428571...

Step 3: Subtract the original x from this equation to eliminate the repeating part: 1000000x - x = 428571.428571... - 0.428571... This simplifies to: 999999x = 428571

Step 4: Solve for x by dividing both sides by 999999: x = 428571/999999

Step 5: Simplify the fraction by finding the greatest common divisor (GCD) of 428571 and 999999, which is 142857, and divide both numbers by this GCD: 428571 ÷ 142857 = 3 999999 ÷ 142857 = 7

Thus, x = 3/7 So, 0.428571428571 as a fraction is 3/7.

Important Glossaries for 0.428571428571 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.
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.
Repeating Decimal: A decimal in which a sequence of digits repeats infinitely.