What is 0.67 as a fraction?

Converting decimals to fractions may be useful in life. Let's walk through the process of converting a decimal 0.67 to a fraction.

You can select other values to familiarize yourself with the conversion guide.

Often, convert 0.669 to a fraction or 0.675 to a fraction, depending on the task.

Understanding the decimal: “0.67”

A decimal number has an integer and fractional parts. The decimal point separates the two. The integer is to the left, the fraction to the right. For example, in 0.67, 0 is the integer and 67 is the fraction.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 0.67.
    • By removing the decimal point, we derive the numerator as 67.
  2. For the denominator:
    • Each position after the decimal represents a division by 10.
    • Thus, having 2 positions after the decimal equates to 100 or 102.
  3. Factors:
    • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
    • For instance, the factors of 67 include 1, and 67.
    • The factors of 100 comprise 1, 2, 4, 5, 10, 20, 25, 50, and 100.
  4. Greatest Common Divisor (GCD):
    • It's the largest number that can evenly divide both the numerator and the denominator.
    • In this instance, the GCD for 67 and 100 is 1.

The factors of 67 are:

1 67

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

0.67=0.671=0.67 × 1001 × 100=67100=67÷1100÷1=67100

Solution:

0.67 = 67100

What is a decimal?

A decimal is a numeral system with a point. This point divides the integer from its fractional part. It provides a straightforward way to express and work with values less than one.

What is a fraction?

A fraction is a mathematical expression of two parts: the numerator on top and the denominator below. It represents partial values, showcasing relationships or comparisons.

Step-by-step solution:

  • Step 1 Let's frame our decimal as a fraction over 1. This way we will make the next steps possible. 0.67 = 0.671
  • Step 2: Decimals vary. Some are short; others are long. We will make the number of digits after the decimal point identical. For 0.67, we have three digits. This way we will increase our faction by a factor of 10 for each digit. Factor = 102 = 100
  • Step 3: Taking our coefficient, we need to equalize both the numerator and the denominator. 0.67 × 1001 × 100 = 67100
  • Step 4: Now we need to cut back the 67100. This requires seeking common divisors. Here, 1 our divisor, dividing both parts. 67 ÷ 1100 ÷ 1 = 67100

Answer in mixed fraction format:

0.67 =
67
100