Understanding fractions is a fundamental concept in mathematics, and simplifying them is an essential skill. In this article, we will explore how to convert the decimal number 1.125 into a fraction in its simplest form.
Why Convert Decimals to Fractions?
Decimals and fractions are two different ways to represent numbers, but they both convey the same value. Decimals are often used in calculations and measurements, while fractions are commonly used in mathematical expressions, particularly in algebra and geometry. Converting decimals to fractions can help in simplifying mathematical expressions, making it easier to work with proportions, and providing a clearer understanding of the relationships between numbers.
Steps to Convert 1.125 to a Fraction
To convert 1.125 into a fraction, we can follow these steps:
- Separate the Whole Number: The number 1.125 can be separated into a whole number (1) and a decimal (0.125).
- Determine the Place Value: The decimal 0.125 has three digits after the decimal point, which means it can be expressed as 125/1000.
- Simplify the Fraction: We can simplify the fraction 125/1000 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Simplifying the Fraction
To simplify the fraction 125/1000, we need to find the GCD of 125 and 1000.
The factors of 125 are 1, 5, 25, and 125, while the factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000. The greatest common divisor of 125 and 1000 is 125.
Divide by the GCD
By dividing both the numerator and the denominator by their GCD (125), we can simplify the fraction:
125 ÷ 125 = 1 1000 ÷ 125 = 8
The simplified fraction is 1/8.
Combining the Whole Number and the Fraction
Since we separated the whole number (1) from the decimal (0.125) earlier, we can now combine them:
1 + 1/8 = 1 1/8
Therefore, the decimal number 1.125 can be expressed as a fraction in its simplest form as 1 1/8.
Real-World Applications
Converting decimals to fractions has numerous real-world applications, such as:
- Cooking and Recipes: Fractions are often used in cooking and recipes to represent ingredients and measurements.
- Mathematics and Algebra: Fractions are used to simplify mathematical expressions and solve equations.
- Geometry and Measurement: Fractions are used to represent proportions and measurements in geometry and architecture.
Conclusion
Converting decimals to fractions is an essential skill in mathematics, and simplifying fractions is crucial for working with proportions and mathematical expressions. By following the steps outlined in this article, you can convert the decimal number 1.125 to a fraction in its simplest form, 1 1/8.
We hope this article has helped you understand the process of converting decimals to fractions. If you have any questions or would like to share your thoughts, please leave a comment below.
What is the difference between a decimal and a fraction?
+A decimal is a way to represent a number using a point to separate the whole number from the fractional part. A fraction, on the other hand, is a way to represent a number as a ratio of two integers, with the numerator representing the number of equal parts and the denominator representing the total number of parts.
Why is it important to simplify fractions?
+Simplifying fractions is important because it makes it easier to work with proportions, solve equations, and understand mathematical relationships. Simplified fractions also make it easier to add, subtract, multiply, and divide fractions.
How do I find the greatest common divisor (GCD) of two numbers?
+To find the GCD of two numbers, list the factors of each number and identify the greatest factor they have in common. You can also use the Euclidean algorithm or prime factorization to find the GCD.