What Is 10/99 as a Decimal + Solution With Free Steps

The fraction 10/99 as a decimal is equal to 0.101010.

Fraction expression 10/99 is a proper fraction and is solved through the long division method. As result, we get a recurring decimal value in the quotient that is 0.101010 and a remainder  1 integer value.  

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.

10 99 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 10/99.


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 = 10

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 = 10 $\div$ 99

This is when we go through the Long Division solution to our problem. The following figure shows the long division:

10/99 Long Division Method

Figure 1

10/99 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 10 and 99, we can see how 10 is Smaller than 99, and to solve this division, we require that 10 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 10, which after getting multiplied by 10 becomes 100.

We take this 100 and divide it by 99; this can be done as follows:

 100 $\div$ 99 $\approx$ 1


99 x 1 = 99

This will lead to the generation of a Remainder equal to 100 – 99 = 1. Now this means we have to repeat the process by Converting the 1 into 100 by multiplying the remainder by 10 twice and adding zero in the quotient and solving for that:

100 $\div$ 99 $\approx$ 1 


99 x 1 = 99

This, therefore, produces another Remainder which is equal to 100 – 99 = 1. Now we stop solving this problem. Finally, we have a Quotient generated after combining the pieces of it as 0.101=z, with a Remainder equal to 1.

10_99 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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