Converting the decimal number 0.6 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 0.6 into its simplest fractional form.
Conversion Result
3
5
Original Decimal: 0.6
Value Visualization
Converted Fraction
Here is the step-by-step math to convert it:
1
Let x equal the decimal:
Let x = 0.6
2
Multiply by 10 to eliminate the decimal places:
10x = 6
3
Solve for x:
x = 610
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 (6 and 10).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 10 ÷ 6 = 1 (remainder 4)
Explanation: 6 × 1 = 6. The remainder from 10 - 6 is 4.
• Step 2: 6 ÷ 4 = 1 (remainder 2)
Explanation: 4 × 1 = 4. The remainder from 6 - 4 is 2.
• Step 3: 4 ÷ 2 = 2 (remainder 0)
Explanation: 2 × 2 = 4. The remainder from 4 - 4 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 (6 and 10).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 10 ÷ 6 = 1 (remainder 4)
Explanation: 6 × 1 = 6. The remainder from 10 - 6 is 4.
• Step 2: 6 ÷ 4 = 1 (remainder 2)
Explanation: 4 × 1 = 4. The remainder from 6 - 4 is 2.
• Step 3: 4 ÷ 2 = 2 (remainder 0)
Explanation: 2 × 2 = 4. The remainder from 4 - 4 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 = 6 ÷ 210 ÷ 2 = 35
6
Final fraction conversion result:
Result =
3
5
Conclusion
By following the steps above, we have successfully converted the decimal 0.6 into the simplified fraction 3/5.