 # What Is 17/42 as a Decimal + Solution With Free Steps

The fraction 17/42 as a decimal is equal to 0.404.

The division of two numbers p and q is one of the four fundamental operations in arithmetic. Since it is used often, we sometimes notate the division p $\boldsymbol\div$ q in the form of a fraction p/q, which is easier to write. A fraction is treated the same way as any division. 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 17/42.

## 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 done as follows:

Dividend = 17

Divisor = 42

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 $\div$ 42

This is when we go through the Long Division solution to our problem. Figure 1

## 17/42 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 42, we can see how 17 is Smaller than 42, and to solve this division, we require that 17 be Bigger than 42.

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 42; this can be done as follows:

170 $\div$ 42 $\approx$ 4

Where:

42 x 4 = 168

This will lead to the generation of a Remainder equal to 170 – 168 = 2. Now this means we have to repeat the process by Converting the 2 into 200. This requires a double multiplication by 10 (since 2 x 10 = 20, which is smaller than 200), so we add a 0 to our quotient. Solving for 200:

200 $\div$ 42 $\approx$ 4

Where:

42 x 4 = 168

Finally, we have a Quotient generated after combining the three pieces of it as 0.404, with a Remainder equal to 32. Images/mathematical drawings are created with GeoGebra.