What Is 7/81 as a Decimal + Solution With Free Steps

The fraction 7/81 as a decimal is equal to 0.086.

The ubiquitous nature of the division operation led to the creation of an alternate, more compact way of representing division. This other method is that of a fraction, which is a numeral of the form p/q. This is mathematically equivalent to the familiar p $\boldsymbol\div$ q, where p is now the numerator and q the denominator.

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 7/81.

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 = 81

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 $\div$ 81

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

Figure 1

7/81 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 81, we can see how 7 is Smaller than 81, and to solve this division, we require that 7 be Bigger than 81.

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 81. Therefore, we again multiply by 10 to get 70 x 10 = 700, which is now bigger than 81. 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 81; this can be done as follows:

700 $\div$ 81 $\approx$ 8

Where:

81 x 8 = 648

This will lead to the generation of a Remainder equal to 700 – 648 = 52. Now this means we have to repeat the process by Converting the 52 into 520 and solving for that:

520 $\div$ 81 $\approx$ 6

Where:

81 x 6 = 486

Finally, we have a Quotient generated after combining the three pieces of it as 0.086, with a Remainder equal to 34.

Images/mathematical drawings are created with GeoGebra.