What Is 31/99 as a Decimal + Solution With Free Steps

The fraction 31/99 as a decimal is equal to 0.313.

We know that Division is one of the four primary operators of mathematics and by applying the long division method we can easily convert the fractional form into its equivalent decimal form. When the long division is performed on the fraction 31/99 it results in a recurring decimal.

31 99 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 31/99.


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 = 31

Divisor = 99

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 = 31 $\div$ 99

This is when we go through the Long Division solution to our problem. The solution for fraction 31/99 is shown in the figure below.

31/99 Long Division Method

Figure 1

31/99 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 31 and 99, we can see how 31 is Smaller than 99, and to solve this division, we require that 31 be Bigger than 99.

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 31, which after getting multiplied by 10 becomes 310.

We take this 310 and divide it by 99; this can be done as follows:

 310 $\div$ 99 $\approx$ 3


99 x 3 = 297

This will lead to the generation of a Remainder equal to 310 – 297 = 13. Now this means we have to repeat the process by Converting the 13 into 130 and solving for that:

130 $\div$ 99 $\approx$ 1


99 x 1 = 99

This, therefore, produces another Remainder which is equal to 130 – 99 = 31. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 310.

310 $\div$ 99 $\approx$ 3


99 x 3 = 297

Finally, we have a Quotient generated after combining the three pieces of it as 0.313, with a Remainder equal to 13.Pie Chart 31 by 99 Long Division Method

Images/mathematical drawings are created with GeoGebra. 

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