Converting the decimal number 0.8 into a fraction is a common mathematical operation. In this comprehensive guide, we will walk you through the exact step-by-step process to convert 0.8 into its simplest fractional form.
Conversion Result
4
5
Original Decimal: 0.8
Value Visualization
Converted Fraction
Here is the step-by-step math to convert it:
1
Let x equal the decimal:
Let x = 0.8
2
Multiply by 10 to eliminate the decimal places:
10x = 8
3
Solve for x:
x = 810
4
Calculate the Greatest Common Divisor (GCD) step by step for easy practice on paper:
💡 Manual Calculation Guide (Euclidean Algorithm):
Objective: Find the greatest common divisor that can evenly divide both numbers (8 and 10).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 10 ÷ 8 = 1 (remainder 2)
Explanation: 8 × 1 = 8. The remainder from 10 - 8 is 2.
• Step 2: 8 ÷ 2 = 4 (remainder 0)
Explanation: 2 × 4 = 8. The remainder from 8 - 8 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (2) is the GCD!
→ Conclusion GCD = 2
Objective: Find the greatest common divisor that can evenly divide both numbers (8 and 10).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 10 ÷ 8 = 1 (remainder 2)
Explanation: 8 × 1 = 8. The remainder from 10 - 8 is 2.
• Step 2: 8 ÷ 2 = 4 (remainder 0)
Explanation: 2 × 4 = 8. The remainder from 8 - 8 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (2) is the GCD!
→ Conclusion GCD = 2
5
Simplify the fraction by dividing the numerator and denominator by their GCD (2):
x = 8 ÷ 210 ÷ 2 = 45
6
Final fraction conversion result:
Result =
4
5
Conclusion
By following the steps above, we have successfully converted the decimal 0.8 into the simplified fraction 4/5.