What Is 17/40 as a Decimal + Solution With Free Steps
The fraction 17/40 as a decimal is equal to 0.425.
The division is one of the four basic arithmetic operators in mathematics. Fractions occur when a number is divided by another. The decimal form for such a fraction can be obtained if we perform division in which the numerator act as the dividend and the denominator act as the divisor.
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.
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 17/40.
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 = 40
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 = 17 $\div$ 40
This is when we go through the Long Division solution to our problem. The long division for the fraction under study is shown in figure 1.
17/40 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 40 we can see how 17 is Smaller than 40, and to solve this division we require that 17 be Bigger than 40.
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 17, which after getting multiplied by 10 becomes 170.
We take this 170 and divide it by 40, this can be seen done as follows:
170 $\div$ 40 $\approx$ 4
40 x 4 = 160
This will lead to the generation of a Remainder equal to 170 – 160 = 10, now this means we have to repeat the process by Converting the 10 into 100 and solving for that:
100 $\div$ 40 $\approx$ 2
40 x 2 = 80
This, therefore, produces another remainder which is equal to 100 – 80 = 20. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 200.
200 $\div$ 40 = 5
40 x 5 = 200
Finally, we have a Quotient generated after combining the three pieces of it as 0.425, with a Remainder equal to 0.
Images/mathematical drawings are created with GeoGebra.