What Is 40/42 as a Decimal + Solution With Free Steps
The fraction 40/42 as a decimal is equal to 0.95238095.
Decimal notation can be obtained from fractional representation by applying the division method to it. The fraction 40/42 is a proper fraction simplifying the fraction we get the decimal number 0.952.
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 40/42.
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 = 40
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 = 40 $\div$ 42
This is when we go through the Long Division solution to our problem. The following figure shows the long division:
40/42 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 40 and 42, we can see how 40 is Smaller than 42, and to solve this division, we require that 40 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 40, which after getting multiplied by 10 becomes 400.
We take this 400 and divide it by 42; this can be done as follows:
400 $\div$ 42 $\approx$ 9
42 x 9 = 378
This will lead to generating a Remainder equal to 400 – 378 = 22. Now this means we have to repeat the process by Converting the 22 into 220 and solving for that:
220 $\div$ 42 $\approx$ 5
42 x 5 = 210
This, therefore, produces another Remainder which is equal to 220 – 210 = 10. Now we must solve this problem to the Third Decimal Place for accuracy, so we repeat the process with dividend 100.
100 $\div$ 42 $\approx$ 2
42 x 2 = 84
Finally, we have a Quotient generated after combining the three pieces of it as 0.952=z, with a Remainder equal to 16.
Images/mathematical drawings are created with GeoGebra.