 # What Is 1/21 as a Decimal + Solution With Free Steps

The fraction 1/21 as a decimal is equal to 0.047619047619.

The three forms of Fractions are proper fractions, improper fractions, and mixed fractions. Proper fractions have a numerator that is less than the denominator, while Improper fractions have a numerator that is greater than the denominator. A Mixed fraction is created by combining an improper fraction with a whole number.

Here, we are more interested in the division types that result in a Decimal value, as this can be expressed as a Fraction. We see fractions as a way of showing two numbers having the operation of Division between them that result in a value that lies between two Integers. Now, we introduce the method used to solve said fraction to decimal conversion, called Long Division, which we will discuss in detail moving forward. So, let’s go through the Solution of fraction 1/21.

## Solution

First, we convert the fraction components, i.e., the numerator and the denominator, and transform them into the division constituents, i.e., the Dividend and the Divisor, respectively.

This can be done as follows:

Dividend = 1

Divisor = 21

Now, we introduce the most important quantity in our division process: the Quotient. The value represents the Solution to our division and can be expressed as having the following relationship with the Division constituents:

Quotient = Dividend $\div$ Divisor = 1 $\div$ 21

This is when we go through the Long Division solution to our problem. Figure 1

## 1/21 Long Division Method

We start solving a problem using the Long Division Method by first taking apart the division’s components and comparing them. As we have 1 and 21, we can see how 1 is Smaller than 21, and to solve this division, we require that 1 be Bigger than 21.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. If so, we calculate the Multiple of the divisor closest to the dividend and subtract it from the Dividend. This produces the Remainder, which we then use as the dividend later.

Now, we begin solving for our dividend 1, which after getting multiplied by 10 becomes 10.

Still, the dividend is less than the divisor, so we will multiply it by 10 again. For that, we have to add the zero in the quotient. So, by multiplying the dividend by 10 twice in the same step and by adding zero after the decimal point in the quotient, we now have a dividend of 100

We take this 100 and divide it by 21; this can be done as follows:

100 $\div$ 21 $\approx$ 4

Where:

21 x 4 = 84

This will lead to the generation of a Remainder equal to 100 – 84 = 16. Now this means we have to repeat the process by Converting the 16 into 160 and solving for that:

160 $\div$ 21 $\approx$ 7

Where:

21 x 7 = 147

Finally, we have a Quotient generated after combining the pieces of it as 0.047=z, with a Remainder equal to 13. Images/mathematical drawings are created with GeoGebra.