What is 1.9 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 1.9 to a fraction.

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

Often, convert 1.89 to a fraction or 1.91 to a fraction, depending on the task.

Understanding the decimal: “1.9”

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 1.9, 1 is the integer part and 9 is the fractional part.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 1.9.
    • By removing the decimal point, we derive the numerator as 19.
  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 19 include 1, and 19.
    • 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 19 and 10 is 1.

The factors of 19 are:

1 19

The factors of 10 are:

1 2 5 10

Conversion formula (equation):

1.9=1.91=1.9 × 101 × 10=1910=19÷110÷1=1910


1.9 = 1910

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. 1.9 = 1.91
  • Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 1.9, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 101 = 10
  • Step 3: Using this factor, multiply both the numerator and the denominator. 1.9 × 101 × 10 = 1910
  • Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 1. Divide both the numerator and the denominator by this common divisor. 19 ÷ 110 ÷ 1 = 1910

Answer in mixed fraction format:

1.9 =