What is 3.117 as a Fraction?

Understanding 3.117 as a Fraction in 6 Simple Steps

1. Separate the whole number and the decimal

The original number we're dealing with is 3.117. This number is not just a decimal, it's a combination of a whole number and a decimal. In other words, it's a mixed number - a number that includes both a whole number and a fraction.

In 3.117, the number to the left of the decimal point is the whole number part, and the number to the right is the decimal part. So in this case:

• The whole number part is "3"
• The decimal part is "117"

This is significant because in our next steps we're going to treat these two parts separately.

2. 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 3.117 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):

• 1 is at the tenths place
• 1 is at the hundredths place
• 7 is at the thousandths place

3. Write the decimal part as a fraction

Given the decimal 3.117, you'd write it over the place value. This means 117 (the numbers to the right of the decimal point) over 1000 (denoting its place value).

This gives 117/1000 as the initial fraction.

4. 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 3, which is 117/1000.

How do you find the GCD of 117 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 117 are 3, 3, 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:
  • There are no common factors between 117 and 1000. So, we'll take 1 as the common factor as both numbers are divible by it.

Hence, the GCD of 117 and 1000 is 1.

Now, divide both the numerator and the denominator of the fraction by their GCD (1) to simplify the fraction.

• 117 ÷ 1 = 117
• 1000 ÷ 1 = 1000

Therefore, the fraction 117/1000 simplifies to 117/1000.

5. Combine the whole number and the fraction

Now, just combine the whole number and the fraction. In this case, combine 3 and 117/1000 to make the mixed number 3117/1000.

6. Convert to improper fraction

Lastly, we want to convert this mixed number into a fraction. The numerator of this fraction will be calculated by (Whole Number * Denominator of the fraction) + Numerator of the fraction:

(3 * 1000) + 117 = 3117

The denominator of our improper fraction is the same as the denominator of the fraction in step 5. So, the denominator is 1000.

Put it together: The improper fraction is 3117/1000.

So, the decimal 3.117 is equivalent to the mixed number 3117/1000 which can be represensted as an improper fraction 3117/1000.