What Is 7/84 as a Decimal + Solution With Free Steps
The fraction 7/84 as a decimal is equal to 0.083.
We use the basic arithmetic operation of division a lot in daily life. It is easier to write and represent it in the form of a fraction, a numeral of the form p/q. Here, p is the numerator and q is the denominator. Mathematically, evaluating fractions is the same as evaluating a 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 7/84.
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 = 7
Divisor = 84
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 = 7 $\div$ 84
This is when we go through the Long Division solution to our problem.
Figure 1
7/84 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 7 and 84, we can see how 7 is Smaller than 84, and to solve this division, we require that 7 be Bigger than 84.
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.
However, in our case, 7 x 10 = 70 which is still smaller than 84. Therefore, we again multiply by 10 to get 70 x 10 = 700, which is now bigger than 84. To indicate this second multiplication by 10, we add a 0 after the decimal point in our quotient.
Now, we begin solving for our dividend 7, which after getting multiplied by 100 becomes 700.
We take this 700 and divide it by 84; this can be done as follows:
700 $\div$ 84 $\approx$ 8
Where:
84 x 8 = 672
This will lead to the generation of a Remainder equal to 700 – 672 = 28. Now this means we have to repeat the process by Converting the 28 into 280 and solving for that:
280 $\div$ 84 $\approx$ 3
Where:
84 x 3 = 252
Finally, we have a Quotient generated after combining the three pieces of it as 0.083, with a Remainder equal to 28.
Images/mathematical drawings are created with GeoGebra.