10.333333333 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. The numbers in decimal are expressed with a decimal point (.), and for example, 10.333333333, we are going to learn how to convert a decimal to a fraction.

What is 10.333333333 as a Fraction?

$10.333333333 as a fraction$

Answer

The answer for 10.333333333 as a fraction is 31/3.

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: Identify the repeating part of the decimal. Here, 0.333333... is the repeating part.

Step 2: Let x = 10.333333...

Step 3: Multiply x by 10 to shift the decimal point for the repeating part: 10x = 103.333333...

Step 4: Subtract the original x from 10x to eliminate the repeating part: 10x - x = 103.333333... - 10.333333... 9x = 93

Step 5: Solve for x by dividing both sides by 9: x = 93/9

Step 6: Simplify the fraction 93/9. The GCD of 93 and 9 is 3. 93/9 = 31/3

Hence, 10.333333333 can be written as a fraction 31/3.

Important Glossaries for 10.333333333 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 in which a digit or group of digits repeats 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.