Write The Decimals As Proper Fractions Or Mixed Numbers And Simplify.a. 0.847 B. -0.0025 C. 4.16

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Introduction

In mathematics, decimals are a way of representing numbers in a specific format. They are used to express fractions and mixed numbers in a more compact form. However, in many mathematical operations and applications, it is often necessary to convert decimals back into their equivalent fractions or mixed numbers. This process can be a bit challenging, but with the right techniques and strategies, it can be done efficiently. In this article, we will explore how to write decimals as proper fractions or mixed numbers and simplify them.

Writing Decimals as Proper Fractions

A proper fraction is a fraction where the numerator is less than the denominator. To write a decimal as a proper fraction, we need to follow these steps:

  1. Determine the place value of the decimal: Identify the place value of the decimal, such as tenths, hundredths, or thousandths.
  2. Determine the numerator and denominator: The numerator is the number before the decimal point, and the denominator is the place value of the decimal.
  3. Write the fraction: Write the fraction with the numerator and denominator.

For example, let's consider the decimal 0.847. To write this decimal as a proper fraction, we need to follow the steps above:

  1. Determine the place value of the decimal: The decimal 0.847 has a place value of hundredths.
  2. Determine the numerator and denominator: The numerator is 847, and the denominator is 100.
  3. Write the fraction: The fraction is 847/100.

Writing Decimals as Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction. To write a decimal as a mixed number, we need to follow these steps:

  1. Determine the whole number part: Identify the whole number part of the decimal.
  2. Determine the proper fraction part: Identify the proper fraction part of the decimal.
  3. Write the mixed number: Write the mixed number with the whole number part and the proper fraction part.

For example, let's consider the decimal 4.16. To write this decimal as a mixed number, we need to follow the steps above:

  1. Determine the whole number part: The whole number part of the decimal 4.16 is 4.
  2. Determine the proper fraction part: The proper fraction part of the decimal 4.16 is 0.16.
  3. Write the mixed number: The mixed number is 4 16/100.

Simplifying Decimals

Simplifying decimals involves reducing the fraction to its simplest form. To simplify a decimal, we need to follow these steps:

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

For example, let's consider the decimal 0.847. To simplify this decimal, we need to follow the steps above:

  1. Find the GCD: The GCD of 847 and 100 is 1.
  2. Divide the numerator and denominator by the GCD: The new numerator is 847, and the new denominator is 100.
  3. Write the simplified fraction: The simplified fraction is 847/100.

Example 1: Writing Decimals as Proper Fractions

Write the decimal 0.625 as a proper fraction.

To write the decimal 0.625 as a proper fraction, we need to follow the steps above:

  1. Determine the place value of the decimal: The decimal 0.625 has a place value of hundredths.
  2. Determine the numerator and denominator: The numerator is 625, and the denominator is 100.
  3. Write the fraction: The fraction is 625/100.

Example 2: Writing Decimals as Mixed Numbers

Write the decimal 3.75 as a mixed number.

To write the decimal 3.75 as a mixed number, we need to follow the steps above:

  1. Determine the whole number part: The whole number part of the decimal 3.75 is 3.
  2. Determine the proper fraction part: The proper fraction part of the decimal 3.75 is 0.75.
  3. Write the mixed number: The mixed number is 3 75/100.

Example 3: Simplifying Decimals

Simplify the decimal 0.875.

To simplify the decimal 0.875, we need to follow the steps above:

  1. Find the GCD: The GCD of 875 and 100 is 25.
  2. Divide the numerator and denominator by the GCD: The new numerator is 35, and the new denominator is 4.
  3. Write the simplified fraction: The simplified fraction is 35/4.

Conclusion

In this article, we have explored how to write decimals as proper fractions or mixed numbers and simplify them. We have discussed the steps involved in writing decimals as proper fractions, mixed numbers, and simplifying them. We have also provided examples to illustrate the concepts. By following these steps and techniques, you can efficiently convert decimals back into their equivalent fractions or mixed numbers.

References

  • [1] "Decimals and Fractions" by Math Open Reference
  • [2] "Writing Decimals as Fractions" by Khan Academy
  • [3] "Simplifying Decimals" by Purplemath

Keywords

  • decimals
  • fractions
  • mixed numbers
  • simplifying decimals
  • proper fractions
  • mixed numbers
  • greatest common divisor (GCD)
  • numerator
  • denominator

Introduction

In our previous article, we explored how to write decimals as proper fractions or mixed numbers and simplify them. In this article, we will answer some frequently asked questions (FAQs) related to decimals, fractions, and mixed numbers.

Q&A

Q1: What is the difference between a decimal and a fraction?

A1: A decimal is a way of representing a number in a specific format, where the decimal point separates the whole number part from the fractional part. A fraction, on the other hand, is a way of representing a number as a ratio of two integers, where the numerator is the number before the decimal point and the denominator is the place value of the decimal.

Q2: How do I write a decimal as a proper fraction?

A2: To write a decimal as a proper fraction, you need to follow these steps:

  1. Determine the place value of the decimal.
  2. Determine the numerator and denominator.
  3. Write the fraction with the numerator and denominator.

For example, to write the decimal 0.625 as a proper fraction, you would follow these steps:

  1. Determine the place value of the decimal: The decimal 0.625 has a place value of hundredths.
  2. Determine the numerator and denominator: The numerator is 625, and the denominator is 100.
  3. Write the fraction: The fraction is 625/100.

Q3: How do I write a decimal as a mixed number?

A3: To write a decimal as a mixed number, you need to follow these steps:

  1. Determine the whole number part of the decimal.
  2. Determine the proper fraction part of the decimal.
  3. Write the mixed number with the whole number part and the proper fraction part.

For example, to write the decimal 3.75 as a mixed number, you would follow these steps:

  1. Determine the whole number part: The whole number part of the decimal 3.75 is 3.
  2. Determine the proper fraction part: The proper fraction part of the decimal 3.75 is 0.75.
  3. Write the mixed number: The mixed number is 3 75/100.

Q4: How do I simplify a decimal?

A4: To simplify a decimal, you need to follow these steps:

  1. Find the greatest common divisor (GCD) of the numerator and denominator.
  2. Divide the numerator and denominator by the GCD.
  3. Write the simplified fraction with the new numerator and denominator.

For example, to simplify the decimal 0.875, you would follow these steps:

  1. Find the GCD: The GCD of 875 and 100 is 25.
  2. Divide the numerator and denominator by the GCD: The new numerator is 35, and the new denominator is 4.
  3. Write the simplified fraction: The simplified fraction is 35/4.

Q5: What is the greatest common divisor (GCD)?

A5: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder. It is used to simplify fractions by dividing both the numerator and denominator by the GCD.

Q6: How do I find the GCD of two numbers?

A6: To find the GCD of two numbers, you can use the following methods:

  1. List the factors of each number and find the greatest common factor.
  2. Use the Euclidean algorithm to find the GCD.
  3. Use a calculator or online tool to find the GCD.

Q7: What is the difference between a proper fraction and a mixed number?

A7: A proper fraction is a fraction where the numerator is less than the denominator. A mixed number, on the other hand, is a combination of a whole number and a proper fraction.

Q8: How do I convert a mixed number to a decimal?

A8: To convert a mixed number to a decimal, you need to follow these steps:

  1. Convert the mixed number to an improper fraction.
  2. Divide the numerator by the denominator.
  3. Write the decimal with the whole number part and the fractional part.

For example, to convert the mixed number 3 75/100 to a decimal, you would follow these steps:

  1. Convert the mixed number to an improper fraction: The improper fraction is 375/100.
  2. Divide the numerator by the denominator: The decimal is 3.75.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to decimals, fractions, and mixed numbers. We hope that this article has provided you with a better understanding of how to write decimals as proper fractions or mixed numbers and simplify them.

References

  • [1] "Decimals and Fractions" by Math Open Reference
  • [2] "Writing Decimals as Fractions" by Khan Academy
  • [3] "Simplifying Decimals" by Purplemath

Keywords

  • decimals
  • fractions
  • mixed numbers
  • simplifying decimals
  • proper fractions
  • mixed numbers
  • greatest common divisor (GCD)
  • numerator
  • denominator
  • improper fractions
  • mixed numbers to decimals