Converting the decimal number 2.625 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 2.625 into its simplest fractional form.
Conversion Result
21
8
Original Decimal: 2.625
Value Visualization
Converted Fraction
Here is the step-by-step math to convert it:
1
Let x equal the decimal:
Let x = 2.625
2
Multiply by 1000 to eliminate the decimal places:
1000x = 2625
3
Solve for x:
x = 26251000
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 (2625 and 1000).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 2625 ÷ 1000 = 2 (remainder 625)
Explanation: 1000 × 2 = 2000. The remainder from 2625 - 2000 is 625.
• Step 2: 1000 ÷ 625 = 1 (remainder 375)
Explanation: 625 × 1 = 625. The remainder from 1000 - 625 is 375.
• Step 3: 625 ÷ 375 = 1 (remainder 250)
Explanation: 375 × 1 = 375. The remainder from 625 - 375 is 250.
• Step 4: 375 ÷ 250 = 1 (remainder 125)
Explanation: 250 × 1 = 250. The remainder from 375 - 250 is 125.
• Step 5: 250 ÷ 125 = 2 (remainder 0)
Explanation: 125 × 2 = 250. The remainder from 250 - 250 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (125) is the GCD!
→ Conclusion GCD = 125
Objective: Find the greatest common divisor that can evenly divide both numbers (2625 and 1000).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 2625 ÷ 1000 = 2 (remainder 625)
Explanation: 1000 × 2 = 2000. The remainder from 2625 - 2000 is 625.
• Step 2: 1000 ÷ 625 = 1 (remainder 375)
Explanation: 625 × 1 = 625. The remainder from 1000 - 625 is 375.
• Step 3: 625 ÷ 375 = 1 (remainder 250)
Explanation: 375 × 1 = 375. The remainder from 625 - 375 is 250.
• Step 4: 375 ÷ 250 = 1 (remainder 125)
Explanation: 250 × 1 = 250. The remainder from 375 - 250 is 125.
• Step 5: 250 ÷ 125 = 2 (remainder 0)
Explanation: 125 × 2 = 250. The remainder from 250 - 250 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (125) is the GCD!
→ Conclusion GCD = 125
5
Simplify the fraction by dividing the numerator and denominator by their GCD (125):
x = 2625 ÷ 1251000 ÷ 125 = 218
6
Final fraction conversion result:
Result =
21
8
Conclusion
By following the steps above, we have successfully converted the decimal 2.625 into the simplified fraction 21/8.