Understanding fractions and decimals is essential for various mathematical operations and problem-solving. In this article, we will explore how to convert the decimal 7.75 into a fraction in its simplest form.
Understanding Decimals and Fractions
Decimals and fractions are two ways to represent part of a whole. A decimal is a number that uses a point to separate the whole part from the fractional part. On the other hand, a fraction is a way to express a part of a whole as a ratio of two integers, with the top number (numerator) indicating the number of equal parts and the bottom number (denominator) indicating the total number of parts.
Converting Decimals to Fractions
Converting decimals to fractions involves finding the place value of the last digit in the decimal and using it as the denominator. The numerator is the decimal number without the decimal point.
Step-by-Step Process
- Identify the place value of the last digit in the decimal.
- Use the place value as the denominator.
- Remove the decimal point and use the resulting number as the numerator.
Converting 7.75 to a Fraction
Using the step-by-step process, we can convert 7.75 to a fraction.
7.75 has two decimal places, which means the last digit is in the hundredths place. Therefore, the denominator is 100.
Removing the decimal point, we get 775 as the numerator.
So, 7.75 can be written as a fraction: 775/100.
Simplifying the Fraction
The fraction 775/100 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 775 and 100 is 25.
Dividing both the numerator and the denominator by 25, we get:
775 ÷ 25 = 31 100 ÷ 25 = 4
So, the simplified fraction is 31/4.
Benefits of Using Fractions
Using fractions has several benefits, including:
- Simplifying complex calculations
- Representing part of a whole in a clear and concise manner
- Enhancing problem-solving skills
Real-World Applications
Fractions are used in various real-world applications, such as:
- Cooking and recipes
- Finance and accounting
- Science and engineering
Conclusion and Final Thoughts
In conclusion, converting decimals to fractions is an essential mathematical operation that can be used in various applications. By following the step-by-step process, we can convert 7.75 to a fraction and simplify it to its simplest form, 31/4.
We hope this article has provided you with a clear understanding of decimals and fractions and how to convert between them. Remember to practice and apply these concepts to improve your problem-solving skills.
Now it's your turn! Take a moment to think about how you can apply the concepts learned in this article to your everyday life. Share your thoughts and questions in the comments below.
We'd love to hear from you and help you with any questions you may have.
What is the difference between a decimal and a fraction?
+A decimal is a number that uses a point to separate the whole part from the fractional part, while a fraction is a way to express a part of a whole as a ratio of two integers.
How do I convert a decimal to a fraction?
+To convert a decimal to a fraction, identify the place value of the last digit in the decimal, use it as the denominator, and remove the decimal point to use the resulting number as the numerator.
What is the simplest form of the fraction 775/100?
+The simplest form of the fraction 775/100 is 31/4.