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What Is 3/23 as a Decimal + Solution With Free Steps

The fraction 3/23 as a decimal is equal to 0.1304.

Rational numbers can be represented in three different ways: as a fraction, as a percentage, or as a decimal. Fractional representation is the most widely used. The fraction 3/23 is a proper 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 3/23.

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 = 3

Divisor = 23

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 = 3 $\div$ 23

This is when we go through the Long Division solution to our problem. The following figure shows the solution for fraction 3/23.

3/23 Long Division Method

Figure 1

3/23 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 3 and 23, we can see how 3 is Smaller than 23, and to solve this division, we require that 3 be Bigger than 23.

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 3, which after getting multiplied by 10 becomes 30.

We take this 30 and divide it by 23; this can be done as follows:

 30 $\div$23 $\approx$ 1

Where:

23 x 1 = 23

This will lead to the generation of a Remainder equal to 30 – 23 = 7. Now this means we have to repeat the process by Converting the 7 into 70 and solving for that:

70 $\div$ 23 $\approx$ 3 

Where:

23 x 3 = 69

This, therefore, produces another Remainder which is equal to 70 – 69 = 1.  After multiplying 1 by 10, we get 10 which is smaller than 23. That means division is not possible. So to make it bigger than 23, the 10 is again multiplied by 10 which gives us 100.

This is done by putting a zero in the quotient after the decimal point. Now, we begin solving for our dividend 100.

100 $\div$ 23 $\approx$ 4 

Where:

23 x 4 = 92

Finally, we have a Quotient generated after combining the four pieces of it as 0.1304, with a Remainder equal to 8.

Images/mathematical drawings are created with GeoGebra.

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