What Is 1/3 as a Decimal + Solution With Free Steps

1by3 As A DecimalThe fraction 1/3 as a decimal is equal to 0.333.

Fractions in mathematics are used to express the operation of division applied across two different numbers, and most of the time, solving a number expressed as a fraction results in a Decimal Value.

There are two types of fractions, Proper and Improper. Proper being ones with a numerator smaller than the denominator, whilst Improper being vice versa. Another important fact about Fractions is that their resulting decimal numbers have a Whole Number part and a Decimal part.

So, now we solve the fraction 1/3, which is given to us.

Solution

The method used for solving divisions normally is the Multiple method, where the dividend is a multiple of the divisor, but to solve fractions we use the Long Division Method.

So, we begin by first extracting the division components out of the Fraction, which is done by comparing them. As we already know, the numerator is equivalent to the Dividend and the denominator to the Divisor.

Dividend = 1

Divisor = 3

Then, we introduce the Quotient which is defined as the solution to a division problem, and for a division is expressed as follows:

Quotient = Dividend $\div$ Divisor= 1 $\div $ 3

Now, we will look at the Long Division solution of our fraction 1/3:

1/3 Long Division Method

Figure 1

1/3 Long Division Method

Long Division Method works by breaking down a division into smaller parts and then solving them part by part until a valid Quotient is acquired. To solve a division using Long Division, we find the Multiple of the divisor which is the closest we can find to the dividend.

Before we move forward, we must introduce the term Remainder, which defines the number which is left behind once you Subtract the multiple of the divisor from the dividend. But that’s not all as this Remainder then becomes the new dividend and we shall solve the next iteration of Division for it.

Finally, we begin by solving our problem 1/3. First, we take the proper fraction’s dividend and make it bigger using the Decimal Point, as it adds a zero to it. This makes the dividend equal to 10, and the solution goes forward as:

 10 $\div$ 3 $\approx$ 3

Where:

 3 x 3 = 9 

So, a Remainder equal to 10 – 9 = 1 is produced. Hence, we repeat the process as we don’t have a conclusive result yet, so the dividend again becomes 10 by adding the Zero to the remainder. Now, the solution goes forward as:

10 $\div$ 3 $\approx$ 3

Where:

3 x 3 = 9 

Now, if we look at the remainder, we notice it is Repeating. As we had a remainder equal to 1 in the last iteration, we got the same result here.

Hence, we conclude our division with the Quotient 0.333 as this is a Repeating Decimal Value and will keep repeating to infinity with the Remainder equal to 1.Pie Chart 1 by 3 Long Division Method

Images/mathematical drawings are created with GeoGebra.

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