What is 2.1 as a fraction?

Converting decimals to fractions may be useful in life. Let's walk through the process of converting a decimal 2.1 to a fraction.

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

Often, convert 2.09 to a fraction or 2.11 to a fraction, depending on the task.

Understanding the decimal: “2.1”

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 2.1, 2 is the integer and 1 is the fraction.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 2.1.
    • By removing the decimal point, we derive the numerator as 21.
  2. For the denominator:
    • Each position after the decimal represents a division by 10.
    • Thus, having 1 positions after the decimal equates to 10 or 101.
  3. Factors:
    • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
    • For instance, the factors of 21 include 1, 3, 7, and 21.
    • The factors of 10 comprise 1, 2, 5, and 10.
  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 21 and 10 is 1.

The factors of 21 are:

1 3 7 21

The factors of 10 are:

1 2 5 10

Conversion formula (equation):

2.1=2.11=2.1 × 101 × 10=2110=21÷110÷1=2110

Solution:

2.1 = 2110

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. 2.1 = 2.11
  • Step 2: Decimals vary. Some are short; others are long. We will make the number of digits after the decimal point identical. For 2.1, we have three digits. This way we will increase our faction by a factor of 10 for each digit. Factor = 101 = 10
  • Step 3: Taking our coefficient, we need to equalize both the numerator and the denominator. 2.1 × 101 × 10 = 2110
  • Step 4: Now we need to cut back the 2110. This requires seeking common divisors. Here, 1 our divisor, dividing both parts. 21 ÷ 110 ÷ 1 = 2110

Answer in mixed fraction format:

2.1 =
2
1
10