What is 0.8125 as a fraction?

Converting decimals to fractions may be useful in life. Let's walk through the process of converting a decimal 0.8125 to a fraction.

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

Often, convert 0.812 to a fraction or 0.813 to a fraction, depending on the task.

Understanding the decimal: “0.8125”

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 0.8125, 0 is the integer and 8125 is the fraction.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 0.8125.
    • By removing the decimal point, we derive the numerator as 8125.
  2. For the denominator:
    • Each position after the decimal represents a division by 10.
    • Thus, having 4 positions after the decimal equates to 10000 or 104.
  3. Factors:
    • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
    • For instance, the factors of 8125 include 1, 5, 13, 25, 65, 125, 325, 625, 1625, and 8125.
    • The factors of 10000 comprise 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, and 10000.
  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 8125 and 10000 is 625.

The factors of 8125 are:

1 5 13 25 65 125 325 625 1625 8125

The factors of 10000 are:

1 2 4 5 8 10 16 20 25 40 50 80 100 125 200 250 400 500 625 1000 1250 2000 2500 5000 10000

Conversion formula (equation):

0.8125=0.81251=0.8125 × 100001 × 10000=812510000=8125÷62510000÷625=1316

Solution:

0.8125 = 1316

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. 0.8125 = 0.81251
  • Step 2: Decimals vary. Some are short; others are long. We will make the number of digits after the decimal point identical. For 0.8125, we have three digits. This way we will increase our faction by a factor of 10 for each digit. Factor = 104 = 10000
  • Step 3: Taking our coefficient, we need to equalize both the numerator and the denominator. 0.8125 × 100001 × 10000 = 812510000
  • Step 4: Now we need to cut back the 812510000. This requires seeking common divisors. Here, 625 our divisor, dividing both parts. 8125 ÷ 62510000 ÷ 625 = 1316

Answer in mixed fraction format:

0.8125 =
13
16