What Is 30/99 as a Decimal + Solution With Free Steps

The fraction 30/99 as a decimal is equal to 0.303.

The fraction 30/99 is a recurring decimal fraction. Any fraction can be written in decimal form by carrying out the division of the numerator by the denominator. The result may end at some point or digits may repeat without any end.

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,Â which we will discuss in detail moving forward. So, letâ€™s go through the Solution of fraction 30/99.

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 = 30

Divisor = 99

Now, we introduce the most important quantity in our division process: theÂ 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 = 30 $\div$ 99

This is when we go through the Long Division solution to our problem. The following figure shows the solution for fraction 30/99.

Figure 1

30/99 Long Division Method

We start solving a problem using the Long Division Method by first taking apart the divisionâ€™s components and comparing them. As we have 30Â and 99, we can see how 30 is Smaller than 99, and to solve this division, we require that 30 be Bigger than 99.

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 30, which after getting multiplied by 10 becomes 300.

We take this 300 and divide it by 99; this can be done as follows:

Â 300 $\div$ 99 $\approx$ 3

Where:

99 x 3 = 297

This will lead to the generation of a Remainder equal to 300 â€“ 297 = 3. After multiplying 3 by 30, we get 30 which is smaller than 99. That means division is not possible. So to make it bigger than 99, the 30 is again multiplied by 10 which gives us 300.

This is done by putting a zero in the quotient after the decimal point. Now, we begin solving for our dividend 300.

300 $\div$ 99 $\approx$ 3

Where:

99 x 3 = 297

Finally, we have a Quotient generated after combining the three pieces of it as 0.303, with a Remainder equal to 3.

Images/mathematical drawings are created with GeoGebra.