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What Is 1/89 as a Decimal + Solution With Free Steps

The fraction 1/89 as a decimal is equal to 0.011.

We commonly encounter the division operation in real-life. The usual notation p $\boldsymbol\div$ q is a little confusing in some cases like the division of long terms and in tables. Fractions are another way of expressing division in a compact form p/q, where p is called the numerator and q is termed 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 1/89.

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 = 1

Divisor = 89

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 = 1 $\div$ 89

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

1/89 Long Division Method

Figure 1

1/89 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 1 and 89, we can see how 1 is Smaller than 89, and to solve this division, we require that 1 be Bigger than 89.

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.

In our case, however, multiplying 1 by 10 gets us 10, which is still smaller than 89. Therefore, we multiply again by 10 to get 10 x 10 = 100, which is now larger than 89. To indicate this second multiplication by 10, we add a 0 directly after the decimal point in the quotient.

Now, we begin solving for our dividend 1, which after getting multiplied by 10 becomes 100.

We take this 100 and divide it by 89; this can be done as follows:

 100 $\div$ 89 $\approx$ 1

Where:

89 x 1 = 89

This will lead to the generation of a Remainder equal to 100 – 89 = 11. Now this means we have to repeat the process by Converting the 11 into 110 and solving for that:

110 $\div$ 89 $\approx$ 1 

Where:

89 x 1 = 89

This, therefore, produces another Remainder which is equal to 110 – 89 = 21. Since we have three decimal places, we stop the division process and combine the three pieces of the Quotient as 0.011, with a final remainder equal to 21.

Images/mathematical drawings are created with GeoGebra.

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