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What Is 10/13 as a Decimal + Solution With Free Steps

The fraction 10/13 as a decimal is equal to 0.769.

A Fraction is a numerical quantity that is not a whole number. A Fraction possesses a numerator and a denominator. Proper, improper and mixed are the types of a fraction. In simple words, arithmetic and fraction simplify big and complex values.

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 10/13.

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 = 10

Divisor = 13

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 $\div$ 13

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

           Figure 1

10/13 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 10 and 13, we can see how 10 is Smaller than 13, and to solve this division, we require that 10 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 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 13; this can be seen done as follows:

 100 $\div$ 13 $\approx$ 7

Where:

13 x 7 = 91

This will lead to the generation of a Remainder equal to 100 – 91 = 9. Now this means we have to repeat the process by Converting the 9 into 90 and solving for that:

90 $\div$ 13 $\approx$ 6 

Where:

13 x 6 = 78

This, therefore, produces another remainder which is equal to 90 – 78 = 12. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 120.

120 $\div$ 13 $\approx$ 9

Where:

13 x 9 = 117

Finally, we have a Quotient generated after combining the three pieces of it as 0.769 = z, with a Remainder equal to 3.

Images/mathematical drawings are created with GeoGebra.

Fractions to Decimals List

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