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How to Find the Decimal Expansion of a Fraction

Oct 13, 2025 by talynt.org 128 views

Introduction

In mathematics, decimal expansion is a way to represent a fraction as a recurring or terminating decimal. It is an essential concept in arithmetic and algebra, and it has numerous applications in various fields, including finance, science, and engineering. In this article, we will focus on the decimal expansion of fractions, specifically the decimal expansion of $$\frac{7}{150}$$.

What is Decimal Expansion?

Decimal expansion is the process of converting a fraction into a decimal by dividing the numerator by the denominator. The result is a decimal number that may be terminating or recurring. A terminating decimal is a decimal that has a finite number of digits after the decimal point, while a recurring decimal is a decimal that has a repeating pattern of digits after the decimal point.

How to Find the Decimal Expansion of a Fraction

To find the decimal expansion of a fraction, we can use long division or a calculator. Long division is a manual method that involves dividing the numerator by the denominator, while a calculator is a quick and easy way to find the decimal expansion of a fraction.

Step 1: Divide the Numerator by the Denominator

To find the decimal expansion of $$\frac{7}{150}$$, we can divide 7 by 150 using long division or a calculator.

Step 2: Write the Decimal Expansion

Once we have divided the numerator by the denominator, we can write the decimal expansion of the fraction. If the result is a terminating decimal, we can write it as a finite decimal. If the result is a recurring decimal, we can write it as a repeating decimal.

Decimal Expansion of $$\frac{7}{150}$$

Using long division or a calculator, we can find that the decimal expansion of $$\frac{7}{150}$$ is $$0.04666 \ldots$$.

Why is the Decimal Expansion of $$\frac{7}{150}$$ $$0.04666 \ldots$$?

The decimal expansion of $$\frac{7}{150}$$ is $$0.04666 \ldots$$ because the fraction $$\frac{7}{150}$$ can be written as $$\frac{7}{150} = \frac{7}{2 \cdot 3 \cdot 5^2}$$. Since the denominator has a factor of 5, the decimal expansion of the fraction will have a recurring pattern of 6s.

Conclusion

In conclusion, the decimal expansion of $$\frac{7}{150}$$ is $$0.04666 \ldots$$. This is because the fraction $$\frac{7}{150}$$ can be written as $$\frac{7}{2 \cdot 3 \cdot 5^2}$$, and the denominator has a factor of 5, which results in a recurring pattern of 6s in the decimal expansion.

Answer

The correct answer is C. $$0.04666 \ldots$$.

Discussion

The decimal expansion of fractions is an essential concept in mathematics, and it has numerous applications in various fields. In this article, we have focused on the decimal expansion of $$\frac{7}{150}$$ and have shown that the decimal expansion of this fraction is $$0.04666 \ldots$$. We have also discussed why the decimal expansion of $$\frac{7}{150}$$ is $$0.04666 \ldots$$.

References

[1] "Decimal Expansion" by Math Open Reference. Retrieved from https://www.mathopenref.com/decexp.html
[2] "Long Division" by Khan Academy. Retrieved from <https://www.khanacademy.org/math/algebra/x2f-alg-review/x2f-long-division/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-
Decimal Expansion of Fractions: A Q&A Guide =====================================================

Introduction

In our previous article, we discussed the decimal expansion of fractions, specifically the decimal expansion of $$\frac{7}{150}$$. We showed that the decimal expansion of this fraction is $$0.04666 \ldots$$. In this article, we will answer some frequently asked questions about decimal expansion of fractions.

Q: What is decimal expansion of fractions?

A: Decimal expansion of fractions is the process of converting a fraction into a decimal by dividing the numerator by the denominator. The result is a decimal number that may be terminating or recurring.

Q: How do I find the decimal expansion of a fraction?

A: To find the decimal expansion of a fraction, you can use long division or a calculator. Long division is a manual method that involves dividing the numerator by the denominator, while a calculator is a quick and easy way to find the decimal expansion of a fraction.

Q: What is the difference between terminating and recurring decimals?

A: A terminating decimal is a decimal that has a finite number of digits after the decimal point, while a recurring decimal is a decimal that has a repeating pattern of digits after the decimal point.

Q: How do I know if a decimal is terminating or recurring?

A: To determine if a decimal is terminating or recurring, you can use the following rules:

If the denominator of the fraction has any prime factors other than 2 or 5, the decimal will be recurring.
If the denominator of the fraction has only 2 or 5 as prime factors, the decimal will be terminating.

Q: Can I convert a recurring decimal to a fraction?

A: Yes, you can convert a recurring decimal to a fraction using the following steps:

Identify the recurring pattern of digits.
Multiply the decimal by a power of 10 to shift the recurring pattern to the left of the decimal point.
Subtract the original decimal from the shifted decimal.
Repeat the process until the recurring pattern is eliminated.
The resulting fraction is the decimal expansion of the original fraction.

Q: Can I use a calculator to find the decimal expansion of a fraction?

A: Yes, you can use a calculator to find the decimal expansion of a fraction. Most calculators have a built-in function to convert fractions to decimals.

Q: What are some common mistakes to avoid when finding the decimal expansion of a fraction?

A: Some common mistakes to avoid when finding the decimal expansion of a fraction include:

Not using enough decimal places when performing long division.
Not checking for recurring patterns in the decimal expansion.
Not using a calculator to check the decimal expansion.

Conclusion

In conclusion, decimal expansion of fractions is an essential concept in mathematics, and it has numerous applications in various fields. By understanding the rules and procedures for finding the decimal expansion of fractions, you can avoid common mistakes and ensure accurate results.

Frequently Asked Questions

Q: What is the decimal expansion of $$\frac1}{2}$$? A The decimal expansion of $$\frac{1{2}$$ is 0.5.
Q: What is the decimal expansion of $$\frac1}{3}$$? A The decimal expansion of $$\frac{1{3}$$ is 0.333... (recurring).
Q: What is the decimal expansion of $$\frac1}{4}$$? A The decimal expansion of $$\frac{1{4}$$ is 0.25.
Q: What is the decimal expansion of $$\frac1}{5}$$? A The decimal expansion of $$\frac{1{5}$$ is 0.2.

References

[1] "Decimal Expansion" by Math Open Reference. Retrieved from https://www.mathopenref.com/decexp.html
[2] "Long Division" by Khan Academy. Retrieved from <https://www.khanacademy.org/math/algebra/x2f-alg-review/x2f-long-division/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f-long-division-review/x2f