What is 0.1111111 as a fraction? Tutorial in mathshowcase.info

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 0.1111111 to a fraction.

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

Often, convert 0.111111 to a fraction or 0.11111111 to a fraction, depending on the task.

Understanding the decimal: “0.1111111”

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 0.1111111, 0 is the integer part and 1111111 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 0.1111111.
- By removing the decimal point, we derive the numerator as 1111111.
For the denominator:
- Each position after the decimal represents a division by 10.
- Thus, having 7 positions after the decimal equates to 10000000 or 10⁷.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 1111111 include 1, 239, 4649, and 1111111.
- The factors of 10000000 comprise 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 320, 400, 500, 625, 640, 800, 1000, 1250, 1600, 2000, 2500, 3125, 3200, 4000, 5000, 6250, 8000, 10000, 12500, 15625, 16000, 20000, 25000, 31250, 40000, 50000, 62500, 78125, 80000, 100000, 125000, 156250, 200000, 250000, 312500, 400000, 500000, 625000, 1000000, 1250000, 2000000, 2500000, 5000000, and 10000000.
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 1111111 and 10000000 is 1.

The factors of 1111111 are:

1 239 4649 1111111

The factors of 10000000 are:

1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 125 128 160 200 250 320 400 500 625 640 800 1000 1250 1600 2000 2500 3125 3200 4000 5000 6250 8000 10000 12500 15625 16000 20000 25000 31250 40000 50000 62500 78125 80000 100000 125000 156250 200000 250000 312500 400000 500000 625000 1000000 1250000 2000000 2500000 5000000 10000000

Conversion formula (equation):

$0.1111111 = \frac{0.1111111}{1} = \frac{0.1111111 × 10000000}{1 × 10000000} = \frac{1111111}{10000000} = \frac{1111111÷1}{10000000÷1} = \frac{1111111}{10000000}$

Solution:

0.1111111 = $\frac{1111111}{10000000}$

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. 0.1111111 = $\frac{0.1111111}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.1111111, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10⁷ = 10000000
Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{0.1111111 × 10000000}{1 × 10000000}$ = $\frac{1111111}{10000000}$
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. $\frac{1111111 ÷ 1}{10000000 ÷ 1}$ = $\frac{1111111}{10000000}$

Answer in mixed fraction format:

0.1111111 =

111111

1000000

What is 0.1111111 as a fraction?