What Is 20/21 as a Decimal + Solution With Free Steps

The fraction 20/21 as a decimal is equal to 0.952.

Mixed fractions are formed after simplifying an improper fraction. It consists of an integer number that is completely divided by the improper fractions’ numerator and denominator and a remainder proper fraction coupled together.

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.

20 21 as a decimal

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 20/21.


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 = 20

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 = 20 $\div$ 21

This is when we go through the Long Division solution to our problem. Given is the Long division process in figure 1:

20/21 Long Division Method

Figure 1

20/21 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 20 and 21, we can see how 20 is Smaller than 21, and to solve this division, we require that 20 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 20, which after getting multiplied by 10 becomes 200.

We take this 200 and divide it by 21; this can be done as follows:

 200 $\div$ 21 $\approx$ 9


21 x 9 = 189

This will lead to the generation of a Remainder equal to 200 – 189 = 11. Now this means we have to repeat the process by Converting the 11 into 110 and solving for that:

110 $\div$ 21 $\approx$ 5 


21 x 5 = 105

This, therefore, produces another Remainder which is equal to 110 – 105 = 5. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 50.

50 $\div$ 21 $\approx$ 2 


21 x 2 = 42

Finally, we have a Quotient generated after combining the three pieces of it as 0.952, with a Remainder equal to 8.

20 by 21 Quotient and Remainder 1

Images/mathematical drawings are created with GeoGebra.

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