What Is 7/13 as a Decimal + Solution With Free Steps

The fraction 7/13 as a decimal is equal to 0.538.

The Dividend and Divisor are the numerators and denominators values of a fraction in the long division process respectively. These two values are used to find the result of the fraction in the decimal form, known as the quotient, and whatever that remains at the end is known as the remainder.

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.

7 13 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 7/13.

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 = 7

Divisor = 13

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 = 7 $\div$ 13

This is when we go through the Long Division solution to our problem. The long division is shown below in Figure 1:

7/13 Long Division Method

Figure 1

7/13 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 7, and 13 we can see how 7 is Smaller than 13, and to solve this division we require that 7 be Bigger than 13.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. 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 7, which after getting multiplied by 10 becomes 70.

We take this 70 and divide it by 13, this can be seen done as follows:

 70 $\div$ 13 $\approx$ 5

Where:

13 x 5 = 65

This will lead to the generation of a Remainder equal to 70 – 65 = 5, now this means we have to repeat the process by Converting the 5 into 50 and solving for that:

50 $\div$ 13 $\approx$ 3 

Where:

13 x 3 = 39

This, therefore, produces another remainder which is equal to 50 – 39 = 11. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 110.

110 $\div$ 13 $\approx$ 8 

Where:

13 x 8 = 104

Finally, we have a Quotient generated after combining the three pieces of it as 0.538, with a Remainder equal to 6.

7 by 13 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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