Write As A Fraction In Lowest Terms.$0.85 = \frac{?}{?}$Enter The Numerator And The Denominator.

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Understanding the Problem

Converting a decimal to a fraction is a fundamental concept in mathematics that helps us express numbers in a more precise and meaningful way. In this article, we will focus on converting the decimal 0.85 to a fraction in its lowest terms.

What is a Fraction?

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into.

Converting 0.85 to a Fraction

To convert 0.85 to a fraction, we need to follow these steps:

Step 1: Identify the Decimal

The decimal we want to convert is 0.85.

Step 2: Determine the Place Value

The decimal 0.85 has two digits after the decimal point, which means it has a place value of hundredths.

Step 3: Multiply by the Place Value

To convert the decimal to a fraction, we need to multiply the decimal by the place value. In this case, we multiply 0.85 by 100 (since it has two digits after the decimal point).

0.85 × 100 = 85

Step 4: Write the Fraction

Now that we have the product, we can write the fraction. The numerator is 85, and the denominator is 100.

85/100

Simplifying the Fraction

The fraction 85/100 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 85 and 100 is 5.

85 ÷ 5 = 17 100 ÷ 5 = 20

So, the simplified fraction is:

17/20

Conclusion

Converting a decimal to a fraction is a straightforward process that involves identifying the decimal, determining its place value, multiplying it by the place value, and writing the fraction. In this article, we converted the decimal 0.85 to a fraction in its lowest terms, which is 17/20.

Real-World Applications

Converting decimals to fractions has many real-world applications, such as:

  • Cooking: When a recipe calls for a certain amount of an ingredient, it's often expressed as a decimal. Converting it to a fraction can make it easier to measure and adjust the ingredient.
  • Finance: In finance, decimals are often used to express interest rates, investment returns, and other financial metrics. Converting them to fractions can help investors and financial analysts make more informed decisions.
  • Science: In science, decimals are used to express measurements, such as temperature, pressure, and density. Converting them to fractions can help scientists and researchers make more accurate calculations and predictions.

Tips and Tricks

Here are some tips and tricks to help you convert decimals to fractions:

  • Use a calculator: If you're struggling to convert a decimal to a fraction, use a calculator to help you find the product and simplify the fraction.
  • Look for patterns: Some decimals have patterns that can help you convert them to fractions more easily. For example, the decimal 0.25 can be converted to a fraction by recognizing that it's one-quarter of a whole.
  • Practice, practice, practice: The more you practice converting decimals to fractions, the more comfortable you'll become with the process.

Common Mistakes

Here are some common mistakes to avoid when converting decimals to fractions:

  • Forgetting to multiply by the place value: Make sure to multiply the decimal by the place value to get the correct product.
  • Not simplifying the fraction: Don't forget to simplify the fraction by dividing both the numerator and the denominator by their GCD.
  • Not checking the answer: Always check your answer to make sure it's correct. You can do this by converting the fraction back to a decimal and checking if it matches the original decimal.

Conclusion

Converting decimals to fractions is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can convert decimals to fractions with ease. Remember to practice, practice, practice, and avoid common mistakes to become more confident and proficient in converting decimals to fractions.

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

A: A decimal is a way of expressing a number using a point (.) to separate the whole number part from the fractional part. A fraction, on the other hand, is a way of expressing a part of a whole as a ratio of two numbers.

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 you want to convert.
  2. Determine the place value of the decimal (e.g., hundredths, thousandths).
  3. Multiply the decimal by the place value.
  4. Write the fraction with the product as the numerator and the place value as the denominator.
  5. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, follow these steps:

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

Q: What is the difference between a simplified fraction and a reduced fraction?

A: A simplified fraction is a fraction that has been reduced to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). A reduced fraction is a fraction that has been reduced to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD) and any other common factors.

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

A: Yes, you can convert a decimal to a fraction using a calculator. Simply enter the decimal into the calculator and it will display the fraction in its simplest form.

Q: What are some common mistakes to avoid when converting decimals to fractions?

A: Some common mistakes to avoid when converting decimals to fractions include:

  • Forgetting to multiply the decimal by the place value.
  • Not simplifying the fraction by dividing both the numerator and the denominator by their GCD.
  • Not checking the answer by converting the fraction back to a decimal.

Q: How do I convert a decimal to a fraction with a repeating pattern?

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

  1. Identify the repeating pattern in the decimal.
  2. Let x be the decimal with the repeating pattern.
  3. Multiply x by a power of 10 to shift the decimal point to the right of the repeating pattern.
  4. Subtract the original decimal from the new decimal to eliminate the repeating pattern.
  5. Solve for x to find the fraction.

Q: Can I convert a decimal to a fraction with a negative sign?

A: Yes, you can convert a decimal to a fraction with a negative sign. Simply follow the same steps as converting a positive decimal to a fraction, but include the negative sign in the numerator.

Q: How do I convert a decimal to a fraction with a decimal point in the denominator?

A: To convert a decimal to a fraction with a decimal point in the denominator, follow these steps:

  1. Identify the decimal point in the denominator.
  2. Multiply the numerator and denominator by a power of 10 to shift the decimal point in the denominator to the right of the decimal point in the numerator.
  3. Simplify the fraction by dividing both the numerator and the denominator by their GCD.

Q: Can I convert a decimal to a fraction with a mixed number?

A: Yes, you can convert a decimal to a fraction with a mixed number. Simply follow the same steps as converting a positive decimal to a fraction, but include the mixed number in the numerator.

Q: How do I convert a decimal to a fraction with a complex number?

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

  1. Identify the complex number in the decimal.
  2. Multiply the numerator and denominator by a power of 10 to shift the decimal point to the right of the complex number.
  3. Simplify the fraction by dividing both the numerator and the denominator by their GCD.

Conclusion

Converting decimals to fractions is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can become more confident and proficient in converting decimals to fractions.