What Is 10/11 as a Decimal + Solution With Free Steps

The fraction 10/11 as a decimal is equal to 0.909.

When we divide a number p by another number q, we create a fraction p/q. Here, p is called the numerator and q the denominator. All rational numbers can be expressed as fractions. There are several types of fractions like proper (p < q), improper (p > q), and mixed. 10/11 is a proper fraction as 10 < 11.

Here, we are interested more in the types of division that results 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 11 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 10/11.

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 seen done as follows:

Dividend = 10

Divisor = 11

Now, we introduce the most important quantity in our process of division, this is 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 $\div$ 11

This is when we go through the Long Division solution to our problem.

10/11 Long Division Method

Figure 1

10/11 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 11, we can see that 10 is Smaller than 11, and to solve this division we require that 10 be Bigger than 11.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor now or not. And if it is then we calculate the Multiple of the divisor which is 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, which is greater than 11. To our quotient, we add a decimal point “.” to indicate this multiplication by 10.

We take this 100 and divide it by 11, this can be seen done as follows:

 100 $\div$ 11 $\approx$ 9

So we add 9 to our quotient. Here:

11 x 9 = 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. To do this, we multiply 1 by 10 twice, so we add 0 to the quotient. Solving now:

100 $\div$ 11 $\approx$ 9 

Where:

11 x 9 = 99

We add 9 to our quotient. This, therefore, produces another remainder which is equal to 100 – 99 = 1. We now have up to three decimal places for our Quotient. Combining them, we get 0.909 with a final Remainder equal to 1.Pie Chart 10/11 Long Division Method

Images/mathematical drawings are created with GeoGebra.

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