Converting decimals to fractions is a fundamental concept in mathematics, and it's essential to understand the different methods to tackle this problem. In this article, we'll explore three ways to convert the decimal 0.875 to a fraction.
Understanding Decimals and Fractions
Before diving into the conversion methods, let's quickly review the basics of decimals and fractions. A decimal is a way of representing a number with a fractional part, separated by a decimal point. For example, 0.875 is a decimal number. A fraction, on the other hand, represents a part of a whole as a ratio of two integers, such as 3/4 or 2/3.
Method 1: Converting Decimals to Fractions using Equivalent Ratios
One way to convert 0.875 to a fraction is by using equivalent ratios. Since 0.875 is equal to 875/1000, we can simplify this fraction by finding the greatest common divisor (GCD) of 875 and 1000.
To find the GCD, we can use the Euclidean algorithm or simply list the factors of 875 and 1000. The factors of 875 are 1, 5, 7, 25, 35, 125, 175, and 875. 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 is 125.
Now, we can simplify the fraction 875/1000 by dividing both the numerator and denominator by 125.
875 ÷ 125 = 7 1000 ÷ 125 = 8
So, the simplified fraction is 7/8.
Example Calculation
To verify our answer, let's calculate the decimal equivalent of 7/8.
7 ÷ 8 = 0.875
This confirms that 0.875 is indeed equal to 7/8.
Method 2: Converting Decimals to Fractions using Place Value
Another method to convert 0.875 to a fraction is by using place value. We can express 0.875 as a sum of fractions with different place values.
0.875 = 0.8 + 0.07 + 0.005
Now, we can convert each of these decimal parts to fractions.
0.8 = 8/10 = 4/5 0.07 = 7/100 0.005 = 5/1000
To add these fractions, we need to find a common denominator, which is 1000.
4/5 = 800/1000 7/100 = 70/1000 5/1000 = 5/1000
Now, we can add the fractions.
800/1000 + 70/1000 + 5/1000 = 875/1000
This fraction can be simplified by dividing both the numerator and denominator by 125, resulting in 7/8.
Example Calculation
To verify our answer, let's calculate the decimal equivalent of 7/8.
7 ÷ 8 = 0.875
This confirms that 0.875 is indeed equal to 7/8.
Method 3: Converting Decimals to Fractions using Long Division
The third method to convert 0.875 to a fraction is by using long division. We can divide 875 by 1000 using long division.
The quotient of this division is 7 with a remainder of 75. We can express this as a fraction.
875 ÷ 1000 = 7 + 75/1000
To simplify this fraction, we can divide both the numerator and denominator by 25.
75 ÷ 25 = 3 1000 ÷ 25 = 40
So, the simplified fraction is 7 + 3/40 = 7/8.
Example Calculation
To verify our answer, let's calculate the decimal equivalent of 7/8.
7 ÷ 8 = 0.875
This confirms that 0.875 is indeed equal to 7/8.
Conclusion and Final Thoughts
In this article, we explored three ways to convert the decimal 0.875 to a fraction. We used equivalent ratios, place value, and long division to arrive at the same answer: 7/8. Each method has its own advantages and disadvantages, and it's essential to understand the different approaches to tackle this problem.
Whether you're a student or a professional, converting decimals to fractions is a fundamental skill that can be applied in various mathematical contexts. By mastering these methods, you'll become more confident in your ability to work with fractions and decimals.
We hope this article has been informative and helpful. If you have any questions or feedback, please don't hesitate to comment below.
What is the greatest common divisor (GCD) of 875 and 1000?
+The GCD of 875 and 1000 is 125.
How can I simplify a fraction?
+To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
What is the decimal equivalent of 7/8?
+The decimal equivalent of 7/8 is 0.875.