
Table of Contents
 .875 as a Fraction: Understanding and Simplifying
 Understanding Fractions
 Converting .875 into a Fraction
 Examples and Case Studies
 Example 1: .25
 Example 2: .125
 Q&A
 Q1: What is a decimal fraction?
 Q2: How do I convert a decimal fraction into a percentage?
 Q3: Can all decimal fractions be converted into simplified fractions?
 Q4: How can I check if a fraction is simplified?
 Q5: Can a fraction be simplified to a decimal?
 Summary
When it comes to understanding fractions, many people find themselves struggling with decimal fractions. One such decimal fraction is .875. In this article, we will delve into the world of fractions and explore how to convert .875 into a simplified fraction. We will also provide valuable insights and examples to help you grasp the concept more easily.
Understanding Fractions
Fractions are a fundamental concept in mathematics that represent a part of a whole. They consist of two numbers separated by a line, with the number above the line called the numerator and the number below the line called the denominator. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts that make up the whole.
For example, in the fraction 3/4, the numerator is 3, indicating that we have three parts, and the denominator is 4, indicating that the whole is divided into four equal parts.
Converting .875 into a Fraction
Now, let’s focus on converting the decimal fraction .875 into a simplified fraction. To do this, we need to understand the place value of each digit in the decimal.
The digit to the right of the decimal point is in the tenths place, the digit to the right of that is in the hundredths place, and so on. In the case of .875, the 8 is in the tenths place, the 7 is in the hundredths place, and the 5 is in the thousandths place.
To convert .875 into a fraction, we can follow these steps:
 Write down the decimal as the numerator.
 Write down the place value of the rightmost digit as the denominator.
 Simplify the fraction, if possible.
Applying these steps to .875, we have:
 Numerator: 875
 Denominator: 1000 (since the rightmost digit is in the thousandths place)
Now, let’s simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 875 and 1000 is 125.
Dividing both the numerator and denominator by 125, we get:
 Numerator: 875 ÷ 125 = 7
 Denominator: 1000 ÷ 125 = 8
Therefore, .875 can be simplified to the fraction 7/8.
Examples and Case Studies
Let’s explore a few more examples and case studies to solidify our understanding of converting decimal fractions into simplified fractions.
Example 1: .25
To convert .25 into a fraction, we follow the same steps as before:
 Numerator: 25
 Denominator: 100 (since the rightmost digit is in the hundredths place)
Simplifying the fraction by dividing both the numerator and denominator by their GCD (25), we get:
 Numerator: 25 ÷ 25 = 1
 Denominator: 100 ÷ 25 = 4
Therefore, .25 can be simplified to the fraction 1/4.
Example 2: .125
Converting .125 into a fraction:
 Numerator: 125
 Denominator: 1000 (since the rightmost digit is in the thousandths place)
Simplifying the fraction by dividing both the numerator and denominator by their GCD (125), we get:
 Numerator: 125 ÷ 125 = 1
 Denominator: 1000 ÷ 125 = 8
Therefore, .125 can be simplified to the fraction 1/8.
Q&A
Q1: What is a decimal fraction?
A1: A decimal fraction is a fraction whose denominator is a power of 10. It is represented by a decimal point followed by digits that indicate a part of a whole.
Q2: How do I convert a decimal fraction into a percentage?
A2: To convert a decimal fraction into a percentage, multiply it by 100 and add the percentage symbol (%). For example, .875 as a percentage is 87.5%.
Q3: Can all decimal fractions be converted into simplified fractions?
A3: No, not all decimal fractions can be converted into simplified fractions. Some decimal fractions, such as .333333…, have repeating patterns and cannot be expressed as a finite fraction. These are called recurring decimals.
Q4: How can I check if a fraction is simplified?
A4: To check if a fraction is simplified, divide the numerator and denominator by their GCD. If the result is 1, the fraction is simplified. If not, further simplification is possible.
Q5: Can a fraction be simplified to a decimal?
A5: Yes, a fraction can be simplified to a decimal by dividing the numerator by the denominator. The result will be a decimal representation of the fraction.
Summary
In conclusion, understanding and converting decimal fractions into simplified fractions is an essential skill in mathematics. By following the steps outlined in this article, you can easily convert .875 into the fraction 7/8. Remember to consider the place value of each digit in the decimal and simplify the fraction by dividing both the numerator and denominator by their GCD. With practice and examples, you can become proficient in converting decimal fractions into simplified fractions, expanding your mathematical knowledge and problemsolving abilities.