0.338 as a fraction - displayed side-by-side

What is .338 as a Fraction?

When it comes to transforming decimals to fractions, certain numbers can be more intriguing than others. This guide will show you exactly how to express .338 as a fraction. This guide will not only show you exactly how to express 0.338 into a fraction but also ensure you grasp the method behind it.

And for a swift and seamless conversion of any decimal into a fraction, our Decimal to Fraction Calculator stands ready to assist.

Quick answer: The decimal 0.338 expressed as a fraction is 169/500

Understanding .338 as a Fraction in 3 Simple Steps

1. Determine the Decimal Place Value

The place value of a decimal is determined by the number of digits to the right of the decimal point. In the case of turning 0.338 into a fraction, we find its place value is in the thousandths place because are three digits after the decimal point.

Here is the breakdown of the digits after the decimal point (see image for better understanding):

3 is at the tenths place
3 is at the hundredths place
8 is at the thousandths place

Decimal value of 0.338 displayed on Place Value Chart

2. Write the decimal part as a fraction

Given the decimal 0.338, you'd write it over the place value. This means 338 (the numbers to the right of the decimal point) over 1000 (denoting its place value).

This gives 338/1000 as the initial fraction.

3. Simplify the fraction

To simplify the fraction, you need to find the greatest common divisor (GCD), also known as the greatest common factor (GCF), for both the numerator and the denominator.

Let's use the fraction from Step 2, which is 338/1000.

How do you find the GCD of 338 and 1000? There are several methods to find the GCD of two numbers, including the division method, prime factorization, or using Euclid's algorithm. However, we'll use the prime factorization method as it's often the simplest:

Factorize both numbers into their prime factor. Tip - use our prime factors calculator for quick results:
- The prime factors of 338 are 2, 13, 13
- The prime factors of 1000 are 2, 2, 2, 5, 5, 5
Identify the common factors of both numbers from the prime factors above:
- The common factor between 338 and 1000 is 2
Calculate the GCD: To find the GCD, multiply the common prime factors together: In this case, there is only one common prime factor. So, it'll become the CGD value.

Hence, the GCD of 338 and 1000 is 2.

Now, divide both the numerator and the denominator of the fraction by their GCD (2) to simplify the fraction.