What Is 5/82 as a Decimal + Solution With Free Steps

The fraction 5/82 as a decimal is equal to 0.060.

A Fraction (p/q) indicates that we have to divide the number p by q. therefore p is said to be the dividend and q is said to be the divisor. The three main categories of fractions are Proper Fraction, Improper Fraction, and Mixed Fraction.

5 82 as a decimal

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 5/82.


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 = 5

Divisor = 82

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 = 5 $\div$ 82

This is when we go through the Long Division solution to our problem, as shown in figure 1.

5/82 Long Division Method

5/82 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 5 and 82, we can see how 5 is Smaller than 82, and to solve this division, we require that 5be Bigger than 82.

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 5, which after getting multiplied by 10 becomes 50.

We take this 50 and divide it by 82; this can be done as follows:

 50 $\div$ 82 $\approx$ 0


82 x 0 = 0

This will lead to the generation of a Remainder equal to 50 – 0 = 50. Now this means we have to repeat the process by Converting the 50 into 500 and solving for that:

 500 $\div$ 82 $\approx$ 6


82 x 6 = 492

This, therefore, produces another Remainder which is equal to 500 – 492 = 8. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 80.

 80 $\div$ 82 $\approx$ 0


82 x 0 = 0

Finally, we have a Quotient generated after combining the three pieces of it as 0.060=z, with a Remainder equal to 80.Pie Chart 5 by 82 Long Division Method

Images/mathematical drawings are created with GeoGebra.

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