8.3333333 as a Fraction

Professor Greenline Explaining Math Concepts

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Intermediate

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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; numbers in decimal are expressed with a decimal point (.), for example, 8.3333333. We are going to learn how to convert a repeating decimal to a fraction.

What is 8.3333333 as a Fraction?

$8.3333333 as a fraction$

Answer

The answer for 8.3333333 as a fraction is 25/3.

Explanation

Converting a repeating decimal to a fraction involves a few steps. Follow the steps below to find the answer.

Step 1: Let x = 8.3333333...

Step 2: Since one digit is recurring, multiply both sides by 10 to shift the decimal point one place to the right: 10x = 83.3333333...

Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 83.3333333... - 8.3333333... 9x = 75

Step 4: Solve for x by dividing both sides by 9: x = 75/9

Step 5: Simplify the fraction by finding the GCD of 75 and 9, which is 3, and divide both the numerator and the denominator by 3: 75/9 = 25/3

Thus, 8.3333333 can be written as a fraction 25/3.

Important Glossaries for 8.3333333 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 with digits that repeat 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.