What is .075 as a Fraction?

Understanding .075 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 0.075 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):

• 0 is at the tenths place
• 7 is at the hundredths place
• 5 is at the thousandths place

2. Write the decimal part as a fraction

Given the decimal 0.075, you'd write it over the place value. This means 075 (the numbers to the right of the decimal point) over 1000 (denoting its place value).

This gives 75/1000 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 75/1000.

How do you find the GCD of 75 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 75 are 3, 5, 5
  • 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 factors between 75 and 1000 are 5, 5
• Calculate the GCD: To find the GCD, multiply the common prime factors together:
  • 5 * 5 = 25

Hence, the GCD of 75 and 1000 is 25.

Now, divide both the numerator and the denominator of the fraction by their GCD (25) to simplify the fraction.

• 75 ÷ 25 = 3
• 1000 ÷ 25 = 40

Therefore, the fraction 75/1000 simplifies to 3/40.

So, the decimal 0.075 as a fraction is 3/40 when simplified.