How Do You Write 1 11 \frac{1}{11} 11 1 ​ As A Decimal?A. 0. 1 ‾ 0.\overline{1} 0. 1 B. 0.0 6 ‾ 0.0\overline{6} 0.0 6 C. 0. 09 ‾ 0.\overline{09} 0. 09 D. 0.0 5 ‾ 0.0\overline{5} 0.0 5

Introduction

Converting fractions to decimals is an essential skill in mathematics, and it's often used in various real-world applications. In this article, we will focus on converting the fraction $\frac{1}{11}$ to a decimal. We will explore the different methods of conversion and provide a step-by-step guide on how to do it.

Understanding the Fraction

Before we dive into the conversion process, let's understand the fraction $\frac{1}{11}$. This fraction represents the ratio of 1 to 11, where 1 is the numerator and 11 is the denominator. To convert this fraction to a decimal, we need to divide the numerator by the denominator.

Method 1: Long Division

One of the most common methods of converting fractions to decimals is long division. This method involves dividing the numerator by the denominator using long division. Here's how to do it:

Step 1: Set up the long division

To set up the long division, we need to write the numerator (1) on top of a line and the denominator (11) below it.

Step 2: Divide the numerator by the denominator

Next, we need to divide the numerator (1) by the denominator (11). Since 11 is larger than 1, we need to add zeros to the numerator to make it larger.

Step 3: Continue the long division

We continue the long division process by dividing the numerator by the denominator. We need to bring down zeros and continue the division process until we get a remainder of 0.

Method 2: Using a Calculator

Another method of converting fractions to decimals is using a calculator. This method is faster and more accurate than long division. Here's how to do it:

Step 1: Enter the fraction into the calculator

To convert the fraction $\frac{1}{11}$ to a decimal using a calculator, we need to enter the fraction into the calculator.

Step 2: Press the divide button

Next, we need to press the divide button to divide the numerator by the denominator.

Step 3: Get the decimal result

The calculator will display the decimal result of the division.

Method 3: Using a Formula

There is also a formula that can be used to convert fractions to decimals. This formula is based on the concept of infinite geometric series. Here's the formula:

$$\frac{1}{11} = \frac{1}{11} \times \frac{100}{100} = \frac{100}{1100} = \frac{10}{110} = \frac{1}{11}$$

This formula can be used to convert any fraction to a decimal.

Conclusion

Converting fractions to decimals is an essential skill in mathematics. In this article, we have explored three methods of converting fractions to decimals: long division, using a calculator, and using a formula. We have also provided a step-by-step guide on how to convert the fraction $\frac{1}{11}$ to a decimal using each method. By following these methods, you can easily convert fractions to decimals and solve problems in mathematics.

Answer

The correct answer is B. $0.0\overline{6}$.

Explanation

The fraction $\frac{1}{11}$ can be converted to a decimal using the formula:

$$\frac{1}{11} = \frac{1}{11} \times \frac{100}{100} = \frac{100}{1100} = \frac{10}{110} = \frac{1}{11}$$

This formula can be used to convert any fraction to a decimal. The decimal result of the division is $0.0\overline{6}$.

Final Answer

The final answer is B. $0.0\overline{6}$.