0.245 expressed as a fraction is 49/200 in its simplest form. The conversion involves writing 0.245 as 245/1000 (since there are 3 decimal places), then simplifying by dividing numerator and denominator by their GCD of 5. Verification: 49 ÷ 200 = 0.245 ✓
0.245 as a fraction in simplest form is 49/200.
First step: 0.245 = 245/1000 (3 decimal places → denominator 1000).
GCD(245, 1000) = 5 (found by prime factorisation or Euclidean algorithm).
Simplification: 245÷5 = 49 and 1000÷5 = 200, giving 49/200.
Verification: 49 ÷ 200 = 0.245 ✓
GCD(49, 200) = 1, confirming 49/200 is fully simplified.
0.245 = 24.5% = 49:200 ratio.
Step 1: Write 0.245 as a fraction with a power of 10 in the denominator. 0.245 has 3 digits after the decimal point. → Denominator = 10³ = 1000 → 0.245 = 245/1000
Step 2: Find the GCD (Greatest Common Divisor) of 245 and 1000. Factors of 245: 245 = 5 × 49 = 5 × 7² Factors of 1000: 1000 = 8 × 125 = 2³ × 5³ Common factor: 5 GCD(245, 1000) = 5
Step 3: Simplify by dividing both by 5. 245 ÷ 5 = 49 1000 ÷ 5 = 200
Step 4: Check if 49/200 can be simplified further. Factors of 49: 1, 7, 49 (49 = 7²) Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200 (200 = 2³ × 5²) Common factors: only 1 GCD(49, 200) = 1 → already in simplest form.
Answer: 0.245 = 49/200
Confirming that 49/200 = 0.245:
Method 1: Long division 49 ÷ 200: • 49.000 ÷ 200 • 200 goes into 490 twice (2 × 200 = 400): remainder 90 • 200 goes into 900 four times (4 × 200 = 800): remainder 100 • 200 goes into 1000 five times (5 × 200 = 1000): remainder 0 • Result: 0.245 ✓
Method 2: Convert denominator to 1000 49/200 = (49 × 5)/(200 × 5) = 245/1000 = 0.245 ✓
So 49/200 = 0.245 ✓
Method 1: Prime Factorization 245 = 5 × 49 = 5 × 7 × 7 = 5 × 7² 1000 = 10³ = (2 × 5)³ = 2³ × 5³
Common prime factors: 5 (appears in both) GCD = 5
Method 2: Euclidean Algorithm GCD(1000, 245): 1000 = 4 × 245 + 20 GCD(245, 20): 245 = 12 × 20 + 5 GCD(20, 5): 20 = 4 × 5 + 0 GCD = 5 ✓
Since GCD(245, 1000) = 5: 245/1000 ÷ (5/5) = 49/200
0.245 expressed in different ways:
Decimal: 0.245 Fraction (unsimplified): 245/1000 Fraction (simplest form): 49/200 Percentage: 0.245 × 100 = 24.5% Ratio: 49:200 Scientific notation: 2.45 × 10⁻¹
Nearby decimal to fraction conversions: 0.2 = 1/5 0.25 = 1/4 0.245 = 49/200 0.25 = 1/4 = 50/200 0.3 = 3/10
Note: 0.245 lies between 0.24 (= 6/25) and 0.25 (= 1/4).
General rule: • Count the number of decimal places (n). • Write the decimal digits as the numerator, with 10ⁿ as the denominator. • Simplify using the GCD.
Examples: 0.5 → 5/10 → GCD=5 → 1/2 0.25 → 25/100 → GCD=25 → 1/4 0.125 → 125/1000 → GCD=125 → 1/8 0.245 → 245/1000 → GCD=5 → 49/200 0.4 → 4/10 → GCD=2 → 2/5 0.375 → 375/1000 → GCD=125 → 3/8 0.6 → 6/10 → GCD=2 → 3/5 0.75 → 75/100 → GCD=25 → 3/4
0.245 = 245/1000. Find GCD(245, 1000) = 5. Divide: 245÷5 = 49 and 1000÷5 = 200. Simplest form: 49/200. Verification: 49÷200 = 0.245 ✓
GCD(245, 1000) = 5. Using prime factorisation: 245 = 5 × 7² and 1000 = 2³ × 5³. The only common prime factor is 5, so GCD = 5.
Yes. 49 = 7² and 200 = 2³ × 5². They share no common prime factors, so GCD(49, 200) = 1 and 49/200 is in its simplest form.
1. Count the decimal places (n). 2. Write the number without the decimal point as the numerator and 10ⁿ as the denominator. 3. Simplify using the GCD. Example: 0.245 → 245/1000 → ÷5 → 49/200.
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