0.6923076923 as a Fraction

Professor Greenline Explaining Math Concepts

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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, 0.6923076923, we are going to learn how to convert a decimal to a fraction.

What is 0.6923076923 as a Fraction?

$0.6923076923 as a fraction$

Answer

The answer for 0.6923076923 as a fraction will be 9/13.

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: First, recognize that 0.6923076923 is a repeating decimal, specifically 0.692307 repeating. Let x = 0.6923076923...

Step 2: Multiply x by 10^6 (since the repeating part is 6 digits long) to shift the decimal point: 1000000x = 692307.692307...

Step 3: Subtract the original x from this equation: 1000000x - x = 692307.692307... - 0.6923076923... 999999x = 692307

Step 4: Solve for x: x = 692307 / 999999

Step 5: Simplify the fraction by finding the GCD of 692307 and 999999, which is 76923. Divide both the numerator and the denominator by this GCD: (692307 ÷ 76923) / (999999 ÷ 76923) = 9/13

Thus, 0.6923076923 can be written as a fraction 9/13.

Important Glossaries for 0.6923076923 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 fraction in which a figure or group of figures is repeated indefinitely.