Change The Decimal 0.023 To A Fraction And Reduce It To Simplest Terms.A. { \frac{23}{10}$}$B. { \frac{23}{100}$}$C. { \frac{23}{1000}$}$D. None Of These Choices Are Correct.

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Understanding Decimals and Fractions

In mathematics, decimals and fractions are two ways to represent a part of a whole. Decimals are numbers that have a decimal point, while fractions are numbers that have a numerator and a denominator. In this article, we will learn how to convert a decimal to a fraction and reduce it to its simplest terms.

What is a Decimal?

A decimal is a number that has a decimal point. It is a way to represent a part of a whole. For example, 0.023 is a decimal that represents 23 hundredths of a whole.

What is a Fraction?

A fraction is a number that has a numerator and a denominator. It is a way to represent a part of a whole. For example, 23/100 is a fraction that represents 23 hundredths of a whole.

Converting Decimal to Fraction

To convert a decimal to a fraction, we need to follow these steps:

  1. Identify the decimal: Identify the decimal that we want to convert to a fraction. In this case, the decimal is 0.023.
  2. Determine the place value: Determine the place value of the decimal. In this case, the decimal is in the thousandths place.
  3. Write the fraction: Write the fraction with the decimal as the numerator and the place value as the denominator. In this case, the fraction is 23/1000.

Reducing Fractions to Simplest Terms

A fraction is in its simplest terms when the numerator and denominator have no common factors other than 1. To reduce a fraction to its simplest terms, we need to follow these steps:

  1. Find the greatest common factor (GCF): Find the greatest common factor of the numerator and denominator. In this case, the GCF of 23 and 1000 is 1.
  2. Divide the numerator and denominator by the GCF: Divide the numerator and denominator by the GCF. In this case, we divide 23 by 1 and 1000 by 1.
  3. Write the simplified fraction: Write the simplified fraction with the numerator and denominator. In this case, the simplified fraction is 23/1000.

Conclusion

In this article, we learned how to convert a decimal to a fraction and reduce it to its simplest terms. We identified the decimal, determined the place value, wrote the fraction, and reduced the fraction to its simplest terms. We also learned that a fraction is in its simplest terms when the numerator and denominator have no common factors other than 1.

Answer

The correct answer is C. {\frac{23}{1000}$}$.

Discussion

This problem is a great example of how to convert a decimal to a fraction and reduce it to its simplest terms. It requires the student to understand the concept of decimals and fractions and to apply the steps to convert a decimal to a fraction and reduce it to its simplest terms.

Related Topics

  • Converting fractions to decimals
  • Reducing fractions to simplest terms
  • Understanding decimals and fractions

Practice Problems

  1. Convert the decimal 0.045 to a fraction and reduce it to its simplest terms.
  2. Convert the decimal 0.012 to a fraction and reduce it to its simplest terms.
  3. Convert the decimal 0.009 to a fraction and reduce it to its simplest terms.

Solutions

  1. The fraction is 45/1000, which reduces to 9/200.
  2. The fraction is 12/1000, which reduces to 3/250.
  3. The fraction is 9/1000, which reduces to 3/333.33.
    Frequently Asked Questions (FAQs) about Converting Decimals to Fractions ====================================================================

Q: What is a decimal?

A: A decimal is a number that has a decimal point. It is a way to represent a part of a whole.

Q: What is a fraction?

A: A fraction is a number that has a numerator and a denominator. It is a way to represent a part of a whole.

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

A: To convert a decimal to a fraction, follow these steps:

  1. Identify the decimal: Identify the decimal that you want to convert to a fraction.
  2. Determine the place value: Determine the place value of the decimal.
  3. Write the fraction: Write the fraction with the decimal as the numerator and the place value as the denominator.

Q: How do I reduce a fraction to its simplest terms?

A: To reduce a fraction to its simplest terms, follow these steps:

  1. Find the greatest common factor (GCF): Find the greatest common factor of the numerator and denominator.
  2. Divide the numerator and denominator by the GCF: Divide the numerator and denominator by the GCF.
  3. Write the simplified fraction: Write the simplified fraction with the numerator and denominator.

Q: What is the greatest common factor (GCF)?

A: The greatest common factor (GCF) is the largest number that divides both the numerator and denominator of a fraction.

Q: How do I find the GCF of two numbers?

A: To find the GCF of two numbers, follow these steps:

  1. List the factors: List the factors of each number.
  2. Find the common factors: Find the common factors of the two numbers.
  3. Choose the greatest common factor: Choose the greatest common factor of the two numbers.

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

A: A decimal is a number that has a decimal point, while a fraction is a number that has a numerator and a denominator.

Q: Can a decimal be converted to a fraction?

A: Yes, a decimal can be converted to a fraction.

Q: Can a fraction be converted to a decimal?

A: Yes, a fraction can be converted to a decimal.

Q: Why is it important to reduce fractions to their simplest terms?

A: It is important to reduce fractions to their simplest terms because it makes it easier to compare and work with fractions.

Q: How do I compare fractions?

A: To compare fractions, follow these steps:

  1. Find the least common denominator (LCD): Find the least common denominator of the two fractions.
  2. Convert the fractions to have the LCD: Convert the fractions to have the LCD.
  3. Compare the numerators: Compare the numerators of the two fractions.

Q: What is the least common denominator (LCD)?

A: The least common denominator (LCD) is the smallest number that is a multiple of both the denominators of the two fractions.

Q: How do I find the LCD of two numbers?

A: To find the LCD of two numbers, follow these steps:

  1. List the multiples: List the multiples of each number.
  2. Find the common multiples: Find the common multiples of the two numbers.
  3. Choose the least common multiple: Choose the least common multiple of the two numbers.

Q: Can a fraction be equal to a decimal?

A: Yes, a fraction can be equal to a decimal.

Q: Can a decimal be equal to a fraction?

A: Yes, a decimal can be equal to a fraction.

Q: Why is it important to understand decimals and fractions?

A: It is important to understand decimals and fractions because they are used in many real-world applications, such as finance, science, and engineering.