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What Is 17/22 as a Decimal + Solution With Free Steps

The fraction 17/22 as a decimal is equal to 0.772.

A Rational Fraction is a fraction in which both numerator and denominator are polynomials. In contrast, irrational fractions cannot be expressed as fractions. This is the reason they do not have any definite or exact value.  The types of rational fractions include Proper and Improper algebraic fractions.

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 17/22.

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 = 17

Divisor = 22

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 = 17 $\div$ 22

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

          Figure 1

17/22 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 17 and 22, we can see how 17 is Smaller than 22, and to solve this division, we require that 17 be Bigger than 22.

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 17, which after getting multiplied by 10 becomes 170.

We take this 170 and divide it by 22; this can be seen done as follows:

 170 $\div$ 22 $\approx$ 7

Where:

22 x 7 = 154

This will lead to the generation of a Remainder equal to 170 – 154= 16. Now this means we have to repeat the process by Converting the 16 into 160 and solving for that:

160 $\div$ 22 $\approx$ 7

Where:

22 x 7 = 154

This, therefore, produces another remainder which is equal to  160– 154 = 6. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 60.

60$\div$ 22 $\approx$ 2

Where:

22x 2 = 44

Finally, we have a Quotient generated after combining the three pieces of it as 0.772 = z, with a Remainder equal to 16.

Images/mathematical drawings are created with GeoGebra.

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