Study Guides/Maths/0.245 as a Fraction
Study Guide · Maths

Express 0.245 as a Fraction — 0.245 = 49/200

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 ✓

Question (Click to Flip)

Express 0.245 as a fraction in simplest form.

Answer

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 ✓

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Key Facts

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-by-Step: Convert 0.245 to a Fraction

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

Verification

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 ✓

Finding GCD(245, 1000) — Detailed Steps

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 in Other Forms

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 Method for Converting Decimals to Fractions

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

Questions and Answers

Express 0.245 as a fraction in simplest form.+

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 ✓

What is GCD of 245 and 1000?+

GCD(245, 1000) = 5. Using prime factorisation: 245 = 5 × 7² and 1000 = 2³ × 5³. The only common prime factor is 5, so GCD = 5.

Is 49/200 fully simplified?+

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.

How do you convert a decimal to a fraction?+

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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