What is 2.22222 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 2.22222 to a fraction.

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

Often, convert 2.222 to a fraction or 2.225 to a fraction, depending on the task.

Understanding the decimal: “2.22222”

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 2.22222, 2 is the integer part and 22222 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 2.22222.
- By removing the decimal point, we derive the numerator as 222222.
For the denominator:
- Each position after the decimal represents a division by 10.
- Thus, having 5 positions after the decimal equates to 100000 or 10⁵.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 222222 include 1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 37, 39, 42, 66, 74, 77, 78, 91, 111, 143, 154, 182, 222, 231, 259, 273, 286, 407, 429, 462, 481, 518, 546, 777, 814, 858, 962, 1001, 1221, 1443, 1554, 2002, 2442, 2849, 2886, 3003, 3367, 5291, 5698, 6006, 6734, 8547, 10101, 10582, 15873, 17094, 20202, 31746, 37037, 74074, 111111, and 222222.
- The factors of 100000 comprise 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 4000, 5000, 6250, 10000, 12500, 20000, 25000, 50000, and 100000.
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 222222 and 100000 is 2.

The factors of 222222 are:

1 2 3 6 7 11 13 14 21 22 26 33 37 39 42 66 74 77 78 91 111 143 154 182 222 231 259 273 286 407 429 462 481 518 546 777 814 858 962 1001 1221 1443 1554 2002 2442 2849 2886 3003 3367 5291 5698 6006 6734 8547 10101 10582 15873 17094 20202 31746 37037 74074 111111 222222

The factors of 100000 are:

1 2 4 5 8 10 16 20 25 32 40 50 80 100 125 160 200 250 400 500 625 800 1000 1250 2000 2500 3125 4000 5000 6250 10000 12500 20000 25000 50000 100000

Conversion formula (equation):

$2.22222 = \frac{2.22222}{1} = \frac{2.22222 × 100000}{1 × 100000} = \frac{222222}{100000} = \frac{222222÷2}{100000÷2} = \frac{111111}{50000}$

Solution:

2.22222 = $\frac{111111}{50000}$

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. 2.22222 = $\frac{2.22222}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 2.22222, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10⁵ = 100000
Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{2.22222 × 100000}{1 × 100000}$ = $\frac{222222}{100000}$
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. $\frac{222222 ÷ 2}{100000 ÷ 2}$ = $\frac{111111}{50000}$

Answer in mixed fraction format:

2.22222 =

2

11111

50000

What is 2.22222 as a fraction?