Converting the decimal number 0.45 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 0.45 into its simplest fractional form.
Conversion Result
9
20
Original Decimal: 0.45
Value Visualization
Converted Fraction
Here is the step-by-step math to convert it:
1
Let x equal the decimal:
Let x = 0.45
2
Multiply by 100 to eliminate the decimal places:
100x = 45
3
Solve for x:
x = 45100
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 (45 and 100).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 100 ÷ 45 = 2 (remainder 10)
Explanation: 45 × 2 = 90. The remainder from 100 - 90 is 10.
• Step 2: 45 ÷ 10 = 4 (remainder 5)
Explanation: 10 × 4 = 40. The remainder from 45 - 40 is 5.
• Step 3: 10 ÷ 5 = 2 (remainder 0)
Explanation: 5 × 2 = 10. The remainder from 10 - 10 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (5) is the GCD!
→ Conclusion GCD = 5
Objective: Find the greatest common divisor that can evenly divide both numbers (45 and 100).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 100 ÷ 45 = 2 (remainder 10)
Explanation: 45 × 2 = 90. The remainder from 100 - 90 is 10.
• Step 2: 45 ÷ 10 = 4 (remainder 5)
Explanation: 10 × 4 = 40. The remainder from 45 - 40 is 5.
• Step 3: 10 ÷ 5 = 2 (remainder 0)
Explanation: 5 × 2 = 10. The remainder from 10 - 10 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (5) is the GCD!
→ Conclusion GCD = 5
5
Simplify the fraction by dividing the numerator and denominator by their GCD (5):
x = 45 ÷ 5100 ÷ 5 = 920
6
Final fraction conversion result:
Result =
9
20
Conclusion
By following the steps above, we have successfully converted the decimal 0.45 into the simplified fraction 9/20.