Convert 7 9 \frac{7}{9} 9 7 ​ To A Decimal.A. 0.7 B. 0. 7 ‾ 0.\overline{7} 0. 7 C. 0.9 D. 0. 9 ‾ 0.\overline{9} 0. 9

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Introduction

In mathematics, converting fractions to decimals is an essential skill that is used in various mathematical operations. A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number in a base-10 system. In this article, we will focus on converting the fraction 79\frac{7}{9} to a decimal.

What is a Decimal?

A decimal is a way of expressing a number in a base-10 system. It consists of a decimal point and digits that follow it. The digits before the decimal point represent the whole number part, while the digits after the decimal point represent the fractional part.

Converting Fractions to Decimals

To convert a fraction to a decimal, we need to divide the numerator (the top number) by the denominator (the bottom number). In the case of the fraction 79\frac{7}{9}, we need to divide 7 by 9.

Step 1: Divide the Numerator by the Denominator

To divide 7 by 9, we can use long division. Long division is a method of dividing a number by another number by repeatedly subtracting the divisor from the dividend.

Step 2: Write the Result as a Decimal

After performing the long division, we get the result 0.777... . This is a repeating decimal, which means that the digit 7 repeats indefinitely.

What is a Repeating Decimal?

A repeating decimal is a decimal that has a digit or a group of digits that repeats indefinitely. In the case of the decimal 0.777... , the digit 7 repeats indefinitely.

Why is the Decimal 0.777... a Repeating Decimal?

The decimal 0.777... is a repeating decimal because the digit 7 repeats indefinitely. This is due to the fact that the fraction 79\frac{7}{9} has a denominator that is a multiple of 9, which means that the decimal representation of the fraction will have a repeating pattern.

Why is the Decimal 0.777... Not 0.7 or 0.9?

The decimal 0.777... is not 0.7 or 0.9 because the fraction 79\frac{7}{9} is not equal to these decimals. The decimal 0.7 is a terminating decimal, which means that it has a finite number of digits. The decimal 0.9 is also a terminating decimal. However, the decimal 0.777... is a repeating decimal, which means that it has an infinite number of digits.

Conclusion

In conclusion, converting the fraction 79\frac{7}{9} to a decimal results in the repeating decimal 0.777... . This is because the fraction has a denominator that is a multiple of 9, which means that the decimal representation of the fraction will have a repeating pattern. Therefore, the correct answer is B. 0.7‾0.\overline{7}.

Frequently Asked Questions

Q: What is a decimal?

A: A decimal is a way of expressing a number in a base-10 system. It consists of a decimal point and digits that follow it.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator (the top number) by the denominator (the bottom number).

Q: What is a repeating decimal?

A: A repeating decimal is a decimal that has a digit or a group of digits that repeats indefinitely.

Q: Why is the decimal 0.777... a repeating decimal?

A: The decimal 0.777... is a repeating decimal because the digit 7 repeats indefinitely. This is due to the fact that the fraction 79\frac{7}{9} has a denominator that is a multiple of 9, which means that the decimal representation of the fraction will have a repeating pattern.

Q: Why is the decimal 0.777... not 0.7 or 0.9?

A: The decimal 0.777... is not 0.7 or 0.9 because the fraction 79\frac{7}{9} is not equal to these decimals. The decimal 0.7 is a terminating decimal, which means that it has a finite number of digits. The decimal 0.9 is also a terminating decimal. However, the decimal 0.777... is a repeating decimal, which means that it has an infinite number of digits.

References

Introduction

In our previous article, we discussed how to convert the fraction 79\frac{7}{9} to a decimal. We also introduced the concept of repeating decimals and explained why the decimal 0.777... is a repeating decimal. In this article, we will continue to explore the topic of converting fractions to decimals and answer some frequently asked questions.

Q&A Guide

Q: What is the difference between a terminating decimal and a repeating decimal?

A: A terminating decimal is a decimal that has a finite number of digits, while a repeating decimal is a decimal that has an infinite number of digits.

Q: How do I know if a fraction will convert to a terminating decimal or a repeating decimal?

A: If the denominator of the fraction is a power of 2 or 5, the fraction will convert to a terminating decimal. If the denominator is not a power of 2 or 5, the fraction will convert to a repeating decimal.

Q: Can a fraction convert to both a terminating decimal and a repeating decimal?

A: No, a fraction can only convert to either a terminating decimal or a repeating decimal.

Q: How do I convert a fraction to a decimal using a calculator?

A: To convert a fraction to a decimal using a calculator, simply divide the numerator by the denominator.

Q: Can I convert a fraction to a decimal by hand?

A: Yes, you can convert a fraction to a decimal by hand using long division.

Q: What is the benefit of converting fractions to decimals?

A: Converting fractions to decimals can make it easier to perform mathematical operations, such as addition and subtraction.

Q: Can I convert a decimal to a fraction?

A: Yes, you can convert a decimal to a fraction by finding the greatest common divisor (GCD) of the decimal and the denominator.

Q: How do I convert a decimal to a fraction using a calculator?

A: To convert a decimal to a fraction using a calculator, simply press the "frac" button.

Q: Can I convert a fraction to a decimal using a spreadsheet?

A: Yes, you can convert a fraction to a decimal using a spreadsheet by dividing the numerator by the denominator.

Q: What is the difference between a decimal and a percentage?

A: A decimal is a way of expressing a number in a base-10 system, while a percentage is a way of expressing a number as a fraction of 100.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, simply divide the percentage by 100.

Q: Can I convert a decimal to a percentage?

A: Yes, you can convert a decimal to a percentage by multiplying the decimal by 100.

Conclusion

In conclusion, converting fractions to decimals is an essential skill that is used in various mathematical operations. By understanding the difference between terminating decimals and repeating decimals, you can convert fractions to decimals with ease. We hope this Q&A guide has been helpful in answering your questions and providing you with a better understanding of the topic.

Frequently Asked Questions

Q: What is the best way to convert a fraction to a decimal?

A: The best way to convert a fraction to a decimal is to use long division.

Q: Can I convert a fraction to a decimal using a calculator?

A: Yes, you can convert a fraction to a decimal using a calculator by dividing the numerator by the denominator.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, find the greatest common divisor (GCD) of the decimal and the denominator.

Q: What is the benefit of converting fractions to decimals?

A: Converting fractions to decimals can make it easier to perform mathematical operations, such as addition and subtraction.

References