What is 1.1111 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 1.1111 to a fraction.

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

Often, convert 1.111 to a fraction or 1.11111 to a fraction, depending on the task.

Understanding the decimal: “1.1111”

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 1.1111, 1 is the integer part and 1111 is the fractional part.

Conversion Explanation:

1. For the numerator:
   • We start with the number 1.1111.
   • By removing the decimal point, we derive the numerator as 11111.
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 11111 include 1, 41, 271, and 11111.
   • 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 11111 and 10000 is 1.

The factors of 11111 are:

The factors of 10000 are:

Conversion formula (equation):

Solution:

Step-by-step solution:

• Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 1.1111 = $\frac{1.1111}{1}$
• Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 1.1111, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10⁴ = 10000
• Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{\mathrm{1.1111\; \times \; 10000}}{\mathrm{1\; \times \; 10000}}$ = $\frac{11111}{10000}$
• 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. $\frac{\mathrm{11111\; ÷\; 1}}{\mathrm{10000\; ÷\; 1}}$ = $\frac{11111}{10000}$

Answer in mixed fraction format:

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