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 of Converting Decimal Fractions into Fractions

To further solidify our understanding, let’s explore a few more examples of converting decimal fractions into fractions:

### Example 1: .25

Following the steps mentioned earlier:

- 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: .5

Following the steps mentioned earlier:

- Numerator: 5
- Denominator: 10 (since the rightmost digit is in the tenths place)

Simplifying the fraction by dividing both the numerator and denominator by their GCD (5), we get:

- Numerator: 5 ÷ 5 = 1
- Denominator: 10 ÷ 5 = 2

Therefore, .5 can be simplified to the fraction 1/2.

## Why Simplify Fractions?

Simplifying fractions is important because it allows us to express fractions in their simplest form. Simplified fractions are easier to work with in mathematical operations, and they provide a clearer understanding of the relationship between the numerator and denominator.

For example, if we have the fraction 6/8, we can simplify it to 3/4. This simplification helps us see that we have three parts out of a total of four equal parts, making it easier to compare and perform calculations with other fractions.

## Summary

In summary, converting decimal fractions into simplified fractions involves understanding the place value of each digit in the decimal, writing the decimal as the numerator, and writing the place value as the denominator. By simplifying the resulting fraction, we can express decimal fractions in their simplest form.

Remember, when converting .875 into a fraction, we followed these steps:

- Numerator: 875
- Denominator: 1000
- Simplified Fraction: 7/8

By applying these steps, you can convert any decimal fraction into a simplified fraction, allowing for easier calculations and a better understanding of the relationship between the numerator and denominator.

## Q&A

### Q1: What is a decimal fraction?

A1: A decimal fraction is a fraction whose denominator is a power of 10. It is expressed using a decimal point and digits to the right of the decimal point.

### Q2: How do you convert a decimal fraction into a fraction?

A2: To convert a decimal fraction into a fraction, write the decimal as the numerator and the place value of the rightmost digit as the denominator. Simplify the resulting fraction, if possible.

### Q3: Why is it important to simplify fractions?

A3: Simplifying fractions allows for easier calculations and a clearer understanding of the relationship between the numerator and denominator. It helps express fractions in their simplest form.

### Q4: Can all decimal fractions be converted into simplified fractions?

A4: Yes, all decimal fractions can be converted into simplified fractions. However, some decimal fractions may result in repeating or non-terminating decimals when expressed as fractions.

### Q5: How can I check if a fraction is simplified?

A5: To check if a fraction is simplified, ensure that the numerator and denominator have no common factors other