1.3333333333 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. Fractions are one such category. They are always represented in the form of p/q, where p is the numerator and q is the denominator. Fractions represent a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2. Numbers in decimal form are expressed with a decimal point (.), for example, 1.3333333333. We are going to learn how to convert a repeating decimal to a fraction.

1.3333333333 as a Fraction for US Students

What is 1.3333333333 as a Fraction?

$1.3333333333 as a fraction$ Answer

The answer for 1.3333333333 as a fraction is 4/3.

Explanation

Converting a repeating decimal to a fraction can be done systematically. Follow the steps mentioned below to find the answer.

Step 1: Let x = 1.3333333333...

Step 2: Multiply both sides by 10 to shift the decimal point one place to the right. 10x = 13.3333333333...

Step 3: Subtract the original equation (x = 1.3333333333...) from this new equation (10x = 13.3333333333...). 10x - x = 13.3333333333... - 1.3333333333... 9x = 12

Step 4: Solve for x by dividing both sides by 9. x = 12/9

Step 5: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 3. 12/9 = 4/3

Thus, 1.3333333333 can be written as a fraction 4/3.

Important Glossaries for 1.3333333333 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
Repeating Decimal: A decimal in which a digit or group of digits repeats 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 each of the integers in a set without leaving a remainder.