What Is 22/75 as a Decimal + Solution With Free Steps
The fraction 22/75 as a decimal is equal to 0.293.
The fractional form can be converted into its equivalent decimal form by applying the long division method. We know that Division is one of the four primary operators of mathematics hence the long division method is preferred for this conversion.
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 22/75.
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 = 22
Divisor = 75
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 = 22 $\div$ 75
This is when we go through the Long Division solution to our problem. The solution for fraction 22/75 is shown in the following figure.
22/75 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 22 and 75, we can see how 22 is Smaller than 75, and to solve this division, we require that 22 be Bigger than 75.
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 22, which after getting multiplied by 10 becomes 220.
We take this 220 and divide it by 75; this can be done as follows:
220 $\div$ 75 $\approx$ 2
75 x 2 = 150
This will lead to the generation of a Remainder equal to 220 – 150 = 70. Now this means we have to repeat the process by Converting the 70 into 700 and solving for that:
700 $\div$ 75 $\approx$ 9
75 x 9 = 675
This, therefore, produces another Remainder which is equal to 700 – 675 = 25. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 250.
250 $\div$ 75 $\approx$ 3
75 x 3 = 225
Finally, we have a Quotient generated after combining the three pieces of it as 0.293, with a Remainder equal to 25.
Images/mathematical drawings are created with GeoGebra.