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What Is 8/21 as a Decimal + Solution With Free Steps

The fraction 8/21 as a decimal is equal to 0.3809.

Numbers when written in the form of ratios like ‘a/b‘ are known as fractions. They represent the division of two numbers. Rational numbers can be written as fractions but it is not possible for irrational numbers.

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 8/21.

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 = 8

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 = 8 $\div$ 21

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

8/21 Long Division Method

Figure 1

8/21 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 8 and 21, we can see how 8 is Smaller than 21, and to solve this division, we require that 8 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 8, which after getting multiplied by 10 becomes 80.

We take this 80 and divide it by 21; this can be done as follows:

 80 $\div$ 21 $\approx$ 3

Where:

21 x 3 = 63

This will lead to the generation of a Remainder equal to 80 – 63 = 17. Now this means we have to repeat the process by Converting the 17 into 170 and solving for that:

170 $\div$ 21 $\approx$ 8

Where:

21 x 8 = 168

This, therefore, produces another Remainder which is equal to 170 – 168 = 2. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend and make it 20. But 20 is still smaller than the divisor, so we add an extra zero in the quotient to make it 200.

Now division is possible and we repeat the process with the dividend 200.

200 $\div$ 21 $\approx$ 9 

Where:

21 x 9 = 189

Finally, we have a Quotient generated after combining the four pieces of it as 0.3809, with a Remainder equal to 11.

Images/mathematical drawings are created with GeoGebra.

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