Convert 2.1666 to a fraction

Decimal to Fraction Calculator

Result: 2.1666 as a fraction = 5410/2497 or 21666/10000

How to convert 2.1666 to a fraction?

Step 1

The first step of converting any decimal to a fraction is to write it as a fraction.

Put the decimal value as the numerator (the number at the top) and 1 as the denominator (the number at the bottom). No matter what the decimal number is, we always use 1 as the denominator.

2.1666 as 2.1666/1

Step 2

We now multiply both the numerator and the denominator by the power of 10 for every digit there is after the decimal point. We can write this as:

2.1666/1 = 2.1666 x 10000/1 x 10000 = 21666/10000

Step 3

Reduce the fraction into its simplest form, which is when the numerator and denominator cannot be any smaller.

We work out the simplest form by finding the Greatest Common Factor (GCF). A factor is a number that will divide into another without remainder, and the Greatest Common Factor is the largest number that is a factor of two or more numbers.

What we need to do is find the GCF of 21666 and 10000.

The factors of 21666 are: 1, 2, 3, 6, 23, 46, 69, 138, 157, 314, 471, 942, 3611, 7222, 10833, 21666

The factors of 10000 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000

If we look at the two sets of numbers we’ve listed, the Greatest Common Factor for both 21666 and 10000 is: 2

So to reduce the fraction we divide 21666 and 10000 by 2.

21666/10000 = 21666 ÷ 2/10000 ÷ 2 = 10833/5000

Therefore, 2.1666 as a fraction = 5410/2497 or 21666/10000