Rounded To The Nearest Thousandth, What Is The Decimal Equivalent Of $6 \frac{7}{9} \%$?A. 0.067 B. 0.068 C. 0.677 D. 0.678 Please Select The Best Answer From The Choices Provided: A B C D
In mathematics, converting mixed fractions to decimal equivalents is an essential skill that can be applied in various real-world scenarios. A mixed fraction is a combination of a whole number and a proper fraction, and it can be converted to a decimal by performing a series of mathematical operations. In this article, we will explore the process of converting mixed fractions to decimal equivalents, with a focus on the given problem: $6 \frac{7}{9} %$.
Understanding the Problem
The given problem involves converting a mixed fraction to a decimal equivalent. The mixed fraction is $6 \frac7}{9} %$, which can be broken down into two parts{9}$). To convert this mixed fraction to a decimal equivalent, we need to perform the following steps:
- Convert the fractional part to a decimal equivalent.
- Multiply the decimal equivalent of the fractional part by the percentage sign (%).
- Add the result to the whole number part.
Converting the Fractional Part to a Decimal Equivalent
To convert the fractional part ($\frac{7}{9}$) to a decimal equivalent, we can divide the numerator (7) by the denominator (9). This can be done using long division or a calculator.
The decimal equivalent of the fractional part is 0.777... (repeating).
Multiplying the Decimal Equivalent by the Percentage Sign
To multiply the decimal equivalent of the fractional part by the percentage sign (%), we can simply multiply 0.777... by 0.01 (since % is equivalent to 0.01).
Adding the Result to the Whole Number Part
To add the result to the whole number part, we can simply add 0.00777... to 6.
Rounding to the Nearest Thousandth
The problem requires us to round the decimal equivalent to the nearest thousandth. To do this, we can look at the digit in the ten-thousandths place (7). Since this digit is greater than 5, we need to round up the digit in the thousandths place (0) to 1.
Conclusion
In conclusion, the decimal equivalent of $6 \frac{7}{9} %$ is approximately 0.068. This can be verified by converting the mixed fraction to a decimal equivalent using the steps outlined above.
Answer
The correct answer is B. 0.068.
Discussion
This problem requires a strong understanding of mathematical operations, including conversion of mixed fractions to decimal equivalents. It also requires attention to detail and the ability to perform calculations accurately. In real-world scenarios, converting mixed fractions to decimal equivalents can be applied in various fields, such as finance, engineering, and science.
Common Mistakes
When converting mixed fractions to decimal equivalents, common mistakes include:
- Forgetting to multiply the decimal equivalent of the fractional part by the percentage sign (%).
- Not rounding the decimal equivalent to the correct place value.
- Not performing calculations accurately.
Tips and Tricks
To avoid common mistakes and ensure accurate calculations, follow these tips and tricks:
- Use a calculator to perform calculations accurately.
- Double-check your work to ensure that calculations are correct.
- Use a ruler or other straightedge to draw a line under the decimal point to help you keep track of the place value.
Real-World Applications
Converting mixed fractions to decimal equivalents has various real-world applications, including:
- Finance: Converting interest rates from mixed fractions to decimal equivalents can help investors make informed decisions.
- Engineering: Converting mixed fractions to decimal equivalents can help engineers design and build structures that meet specific requirements.
- Science: Converting mixed fractions to decimal equivalents can help scientists measure and analyze data accurately.
Conclusion
In this article, we will address some of the most frequently asked questions related to converting mixed fractions to decimal equivalents.
Q: What is a mixed fraction?
A: A mixed fraction is a combination of a whole number and a proper fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fractional part, and $c$ is the denominator of the fractional part.
Q: How do I convert a mixed fraction to a decimal equivalent?
A: To convert a mixed fraction to a decimal equivalent, you need to follow these steps:
- Convert the fractional part to a decimal equivalent.
- Multiply the decimal equivalent of the fractional part by the percentage sign (%).
- Add the result to the whole number part.
Q: What is the difference between a mixed fraction and a decimal?
A: A mixed fraction is a combination of a whole number and a proper fraction, while a decimal is a numerical value that represents a part of a whole. Mixed fractions can be converted to decimals, but decimals cannot be converted to mixed fractions.
Q: How do I round a decimal equivalent to the nearest thousandth?
A: To round a decimal equivalent to the nearest thousandth, you need to look at the digit in the ten-thousandths place. If this digit is greater than or equal to 5, you need to round up the digit in the thousandths place. If this digit is less than 5, you need to round down the digit in the thousandths place.
Q: What are some common mistakes to avoid when converting mixed fractions to decimal equivalents?
A: Some common mistakes to avoid when converting mixed fractions to decimal equivalents include:
- Forgetting to multiply the decimal equivalent of the fractional part by the percentage sign (%).
- Not rounding the decimal equivalent to the correct place value.
- Not performing calculations accurately.
Q: How do I use a calculator to convert a mixed fraction to a decimal equivalent?
A: To use a calculator to convert a mixed fraction to a decimal equivalent, you need to follow these steps:
- Enter the mixed fraction into the calculator.
- Press the "=" button to calculate the decimal equivalent.
- Round the decimal equivalent to the correct place value.
Q: What are some real-world applications of converting mixed fractions to decimal equivalents?
A: Some real-world applications of converting mixed fractions to decimal equivalents include:
- Finance: Converting interest rates from mixed fractions to decimal equivalents can help investors make informed decisions.
- Engineering: Converting mixed fractions to decimal equivalents can help engineers design and build structures that meet specific requirements.
- Science: Converting mixed fractions to decimal equivalents can help scientists measure and analyze data accurately.
Q: Can I convert a decimal equivalent back to a mixed fraction?
A: Yes, you can convert a decimal equivalent back to a mixed fraction by following these steps:
- Separate the whole number part from the decimal part.
- Convert the decimal part to a fraction.
- Combine the whole number part and the fraction to form a mixed fraction.
Conclusion
In conclusion, converting mixed fractions to decimal equivalents is an essential skill that can be applied in various real-world scenarios. By following the steps outlined above and avoiding common mistakes, you can ensure accurate calculations and make informed decisions.