Converting the fraction 7⁄8 into a decimal is a straightforward process that involves basic division. Let’s break it down step by step to ensure clarity and understanding.
Step-by-Step Conversion
Set Up the Division: Write 7 as the dividend and 8 as the divisor.
( 7 \div 8 )Perform the Division:
- 8 goes into 7 zero times, so we add a decimal point and a zero after 7, making it 70.
- Now, divide 70 by 8:
( 8 \times 8 = 64 )
( 70 - 64 = 6 )
- Bring down another zero, making it 60.
- Divide 60 by 8:
( 8 \times 7 = 56 )
( 60 - 56 = 4 )
- Bring down another zero, making it 40.
- Divide 40 by 8:
( 8 \times 5 = 40 )
( 40 - 40 = 0 )
- 8 goes into 7 zero times, so we add a decimal point and a zero after 7, making it 70.
Final Result: The division yields 0.875.
Thus, 7⁄8 as a decimal is 0.875.
Understanding the Decimal
The decimal 0.875 represents the fraction 7⁄8 in a base-10 numerical system. Each digit after the decimal point corresponds to a power of 10:
- The first digit (8) is in the tenths place ((8 \times 10^{-1})).
- The second digit (7) is in the hundredths place ((7 \times 10^{-2})).
- The third digit (5) is in the thousandths place ((5 \times 10^{-3})).
This representation allows for precise comparisons and calculations in decimal form.
Practical Applications
Understanding 7⁄8 as 0.875 is useful in various contexts:
1. Cooking: If a recipe calls for 7⁄8 cup of sugar, you can measure it as 0.875 cups.
2. Finance: Calculating 7⁄8 of a total amount (e.g., 7⁄8 of 100 = 87.50).
3. Engineering: Converting fractions to decimals for precise measurements.
Comparison with Other Fractions
To put 0.875 in perspective, here’s how it compares to other common fractions:
- 1⁄2 = 0.5
- 3⁄4 = 0.75
- 7⁄8 = 0.875
- 1 = 1.0
7⁄8 is closer to 1 than to 3⁄4, highlighting its position on the number line.
FAQ Section
What is 7/8 as a decimal?
+7/8 as a decimal is 0.875.
How do you convert 7/8 to a percentage?
+Multiply 0.875 by 100 to get 87.5%.
Why is 7/8 important in measurements?
+7/8 is commonly used in construction, sewing, and cooking for precise measurements, often represented as 0.875 inches or cups.
What is the equivalent of 7/8 in a mixed number?
+7/8 is already in its simplest form and cannot be expressed as a mixed number since it is less than 1.
Conclusion
Converting 7⁄8 to 0.875 is a simple yet essential skill in mathematics and everyday life. Whether you’re working with fractions or decimals, understanding this conversion ensures accuracy in calculations and measurements. Mastery of such basics lays the foundation for more complex mathematical concepts.
