What Is .875 as a Fraction? Understanding decimal to fraction conversion is an essential skill in mathematics. If you have ever encountered the decimal .875, you might have wondered how to express it as a fraction. In this comprehensive guide, we will explore how to convert .875 into a fraction, its simplified form, step-by-step calculation methods, and its significance in real-life applications. By the end of this article, you will have a thorough understanding of how decimals and fractions relate to each other.
ALSO READ: What Is .625 as a Fraction?
Understanding Decimals and Fractions
What Are Decimals?
A decimal is a way of representing fractions or parts of a whole using powers of ten. The decimal system is widely used in everyday mathematics, finance, and engineering.
What Are Fractions?
A fraction represents a part of a whole and consists of a numerator (the top number) and a denominator (the bottom number). Fractions can be converted into decimals and vice versa.
Converting .875 to a Fraction
To convert .875 into a fraction, follow these steps:
Step 1: Identify Place Value
The decimal .875 has three digits after the decimal point, which means it is in the thousandths place. This means we can express it as: 875รท1000875 \div 1000
Step 2: Convert to a Fraction
Since .875 is equivalent to 875/1000, we write it as: 8751000\frac{875}{1000}
Step 3: Simplify the Fraction
To simplify 875/1000, we find the greatest common divisor (GCD) of 875 and 1000.
- The factors of 875: 1, 5, 25, 35, 125, 175, 875
- The factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
- The greatest common factor is 125.
Now, divide both the numerator and denominator by 125: 875รท1251000รท125=78\frac{875 \div 125}{1000 \div 125} = \frac{7}{8}
Thus, .875 as a fraction in simplest form is 78\frac{7}{8}.
Methods to Convert .875 to a Fraction
Method 1: Using Place Value
We used place value in the previous section, expressing .875 as 875/1000, then simplifying to 7/8.
Method 2: Converting Using Division
Another method is to take .875 and convert it directly using division:
- Multiply by 1000 to remove the decimal: 875/1000875/1000
- Simplify as we did earlier: 7/8
Method 3: Using a Calculator
You can also use a calculator to convert decimals into fractions. Most scientific calculators have a fraction mode where inputting .875 will return 7/8.
Understanding 7/8 as a Fraction
What Does 7/8 Represent?
The fraction 7/8 means that we have 7 parts out of a total of 8 equal parts. This fraction is commonly used in measurements, probability, and real-world applications.
Decimal and Percentage Equivalent
We can verify our conversion by dividing: 7รท8=0.8757 \div 8 = 0.875 This confirms that .875 is indeed equal to 7/8.
To express it as a percentage: 0.875ร100=87.5%0.875 \times 100 = 87.5\%
Thus, 7/8 is the same as 87.5%.
Real-Life Applications of .875 as a Fraction
In Measurements
- In construction and engineering, measurements like 7/8 inches are commonly used.
- In cooking, ingredient measurements often include fractions like 7/8 cups.
In Finance
- Interest rates or discounts can be expressed as 7/8 of a percentage.
- Stock market fractions sometimes use eighths, so 7/8 is relevant.
In Probability and Statistics
- A probability of 7/8 means a very high chance of an event occurring (87.5%).
Frequently Asked Questions (FAQs)
1. What is .875 as a fraction in simplest form?
Answer: The simplest form of .875 as a fraction is 7/8.
2. How do you convert .875 into a fraction?
Answer: Convert .875 into 875/1000, then simplify by dividing by 125, resulting in 7/8.
3. Is .875 a terminating or repeating decimal?
Answer: .875 is a terminating decimal because it does not go on infinitely.
4. What is .875 as a percentage?
Answer: .875 as a percentage is 87.5%.
5. Can .875 be written as a mixed number?
Answer: No, .875 is a proper fraction because its numerator (7) is smaller than its denominator (8).
6. How do I write .875 in words?
Answer: .875 in words is “eight hundred seventy-five thousandths”.
7. What is 7/8 as a decimal?
Answer: 7 divided by 8 is 0.875.
8. What is 7/8 as a percentage?
Answer: (7/8) ร 100 = 87.5%
9. Is 7/8 greater than 3/4?
Answer: Yes, because 7/8 = 0.875 and 3/4 = 0.75, so 7/8 is greater.
Conclusion
Converting .875 to a fraction is a simple process. By recognizing that .875 is the same as 875/1000, and simplifying it to 7/8, we can see its mathematical and real-world significance. Whether in measurements, finance, or everyday calculations, understanding fractions and decimals enhances numerical literacy. Now that you know how to convert .875 into a fraction, you can apply this knowledge in various fields with confidence!