Write As An Equivalent Decimal Or A Decimal Approximation. Round Your Answer To The Nearest Thousandth.$\[ 2 \frac{13}{17} \\]$\[ 2 \frac{13}{17} = \square \\] (Round To The Nearest Thousandth.)

In mathematics, converting mixed numbers to decimal approximations is an essential skill that helps us perform various calculations and solve problems. A mixed number is a combination of a whole number and a fraction, and converting it to a decimal approximation allows us to work with it more easily. In this article, we will learn how to convert the mixed number $2 \frac{13}{17}$ to its equivalent decimal approximation, rounded to the nearest thousandth.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $2 \frac{3}{4}$ is a mixed number where $2$ is the whole number, $3$ is the numerator, and $4$ is the denominator.

Converting Mixed Numbers to Decimal Approximations

To convert a mixed number to a decimal approximation, we need to follow these steps:

1. Separate the whole number and the fraction: Separate the whole number from the fraction. In the case of $2 \frac{13}{17}$, the whole number is $2$ and the fraction is $\frac{13}{17}$.
2. Convert the fraction to a decimal: To convert the fraction to a decimal, we need to divide the numerator by the denominator. In this case, we need to divide $13$ by $17$.
3. Perform the division: Perform the division to get the decimal approximation of the fraction. In this case, $\frac{13}{17} \approx 0.7647$.
4. Add the whole number: Add the whole number to the decimal approximation of the fraction. In this case, $2 + 0.7647 \approx 2.7647$.

Rounding to the Nearest Thousandth

To round the decimal approximation to the nearest thousandth, we need to look at the digit in the ten-thousandths place. If it is less than $5$, we round down. If it is greater than or equal to $5$, we round up. In this case, the digit in the ten-thousandths place is $7$, which is greater than $5$. Therefore, we round up to $2.765$.

Conclusion

In conclusion, converting mixed numbers to decimal approximations is an essential skill that helps us perform various calculations and solve problems. By following the steps outlined in this article, we can convert the mixed number $2 \frac{13}{17}$ to its equivalent decimal approximation, rounded to the nearest thousandth. The decimal approximation of $2 \frac{13}{17}$ is $2.765$.

Example Problems

Here are some example problems that you can try to practice converting mixed numbers to decimal approximations:

• $3 \frac{14}{25}$
• $4 \frac{23}{32}$
• $5 \frac{17}{24}$

Step-by-Step Solutions

Here are the step-by-step solutions to the example problems:

$3 \frac{14}{25}$

1. Separate the whole number and the fraction: $3$ is the whole number and $\frac{14}{25}$ is the fraction.
2. Convert the fraction to a decimal: $\frac{14}{25} \approx 0.56$.
3. Add the whole number: $3 + 0.56 \approx 3.56$.
4. Round to the nearest thousandth: $3.56$ is already rounded to the nearest thousandth.

$4 \frac{23}{32}$

1. Separate the whole number and the fraction: $4$ is the whole number and $\frac{23}{32}$ is the fraction.
2. Convert the fraction to a decimal: $\frac{23}{32} \approx 0.719$.
3. Add the whole number: $4 + 0.719 \approx 4.719$.
4. Round to the nearest thousandth: $4.719$ is already rounded to the nearest thousandth.

$5 \frac{17}{24}$

1. Separate the whole number and the fraction: $5$ is the whole number and $\frac{17}{24}$ is the fraction.
2. Convert the fraction to a decimal: $\frac{17}{24} \approx 0.708$.
3. Add the whole number: $5 + 0.708 \approx 5.708$.
4. Round to the nearest thousandth: $5.708$ is already rounded to the nearest thousandth.

Practice Problems

Here are some practice problems that you can try to practice converting mixed numbers to decimal approximations:

• $1 \frac{9}{16}$
• $2 \frac{27}{32}$
• $3 \frac{19}{24}$

Answer Key

Here are the answers to the practice problems:

$1 \frac{9}{16}$

$1.5625$

$2 \frac{27}{32}$

$2.84375$

$3 \frac{19}{24}$

$3.792$

Conclusion

In this article, we will answer some frequently asked questions about converting mixed numbers to decimal approximations.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I convert a mixed number to a decimal approximation?

A: To convert a mixed number to a decimal approximation, you need to follow these steps:

1. Separate the whole number and the fraction.
2. Convert the fraction to a decimal by dividing the numerator by the denominator.
3. Add the whole number to the decimal approximation of the fraction.
4. Round the result to the nearest thousandth.

Q: What is the difference between a decimal approximation and an exact value?

A: A decimal approximation is an approximate value of a number, while an exact value is the exact value of a number. For example, the decimal approximation of $\frac{1}{3}$ is $0.3333$, while the exact value of $\frac{1}{3}$ is $0.\overline{3}$.

Q: Why do I need to round to the nearest thousandth?

A: You need to round to the nearest thousandth because it is a common rounding convention in mathematics. Rounding to the nearest thousandth helps to simplify calculations and avoid unnecessary decimal places.

Q: Can I use a calculator to convert a mixed number to a decimal approximation?

A: Yes, you can use a calculator to convert a mixed number to a decimal approximation. However, it is always a good idea to understand the steps involved in converting a mixed number to a decimal approximation, as this will help you to check your calculator's results.

Q: What are some common mistakes to avoid when converting mixed numbers to decimal approximations?

A: Some common mistakes to avoid when converting mixed numbers to decimal approximations include:

• Forgetting to separate the whole number and the fraction.
• Forgetting to convert the fraction to a decimal.
• Forgetting to add the whole number to the decimal approximation of the fraction.
• Rounding incorrectly.

Q: How can I practice converting mixed numbers to decimal approximations?

A: You can practice converting mixed numbers to decimal approximations by working through example problems, such as the ones provided in this article. You can also try converting mixed numbers to decimal approximations on your own, using a calculator or by hand.

Q: What are some real-world applications of converting mixed numbers to decimal approximations?

A: Converting mixed numbers to decimal approximations has many real-world applications, including:

• Calculating percentages and proportions.
• Working with measurements and conversions.
• Solving problems in finance, science, and engineering.

Conclusion

In conclusion, converting mixed numbers to decimal approximations is an essential skill that has many real-world applications. By understanding the steps involved in converting a mixed number to a decimal approximation, you can perform various calculations and solve problems with ease. Practice problems are also provided to help you practice converting mixed numbers to decimal approximations.