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What Is 77/84 as a Decimal + Solution With Free Steps

The fraction 77/84 as a decimal is equal to 0.916.

A recurring decimal is a decimal number in which a digit or group of digits is repeated over and over again forever. All recurring decimals can be written as fractions. The fraction 77/84 is a repeating decimal fraction.

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 77/84.

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 = 77

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 = 77 $\div$ 84

This is when we go through the Long Division solution to our problem. The following figure shows the solution for fraction 77/84.

77/84 Long Division Method

Figure 1

77/84 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 77 and 84, we can see how 77 is Smaller than 84, and to solve this division, we require that 77 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.

Now, we begin solving for our dividend 77, which after getting multiplied by 10 becomes 770.

We take this 770 and divide it by 84; this can be done as follows:

770 $\div$ 84 $\approx$ 9

Where:

84 x 9 = 756

This will lead to the generation of a Remainder equal to 770 – 756 = 14. Now this means we have to repeat the process by Converting the 14 into 140 and solving for that:

140 $\div$ 84 $\approx$ 1 

Where:

84 x 1 = 84

This, therefore, produces another Remainder which is equal to 140 – 84 = 56. Now this means we have to repeat the process by Converting the 56 into 560 and solving for that:

560 $\div$ 64 $\approx$ 6

Where:

64 x 6 = 504

Finally, we have a Quotient generated after combining the three pieces of it as 0.916, with a Remainder equal to 56.

Images/mathematical drawings are created with GeoGebra.

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