What is 1.22 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 1.22 to a fraction.

You can try other values to get more familiar with the conversion process.

Often, convert 1.21 to a fraction or 1.222 to a fraction, depending on the task.

Understanding the decimal: “1.22”

A decimal number consists of an integer part and a fractional part, separated by a decimal point. The integer part is on the left, and the fractional part is on the right. For example, in 1.22, 1 is the integer part and 22 is the fractional part.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 1.22.
    • By removing the decimal point, we derive the numerator as 122.
  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 122 include 1, 2, 61, and 122.
    • 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 122 and 100 is 2.

The factors of 122 are:

1 2 61 122

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

1.22=1.221=1.22 × 1001 × 100=122100=122÷2100÷2=6150

Solution:

1.22 = 6150

What is a decimal?

A decimal is a numeral system that includes a point to separate the whole number part from the fractional part. This system makes it easy to work with numbers less than one.

What is a fraction?

A fraction is a mathematical way of showing a part of a whole. It has two parts: the numerator on top and the denominator below, which help express partial values and comparisons.

Step-by-step solution:

  • Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 1.22 = 1.221
  • Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 1.22, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 102 = 100
  • Step 3: Using this factor, multiply both the numerator and the denominator. 1.22 × 1001 × 100 = 122100
  • Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 2. Divide both the numerator and the denominator by this common divisor. 122 ÷ 2100 ÷ 2 = 6150

Answer in mixed fraction format:

1.22 =
1
11
50