Conversions
Comprehensive notes, formulas, and practice questions for Conversions.
Conversions
Fraction–Decimal Conversions
What you'll learn
- How to write a fraction as a decimal by division (numerator ÷ denominator).
- How to write a decimal as a fraction using place-value names.
- To recognise terminating vs repeating decimals at Class 6 level.
- To use conversions in money, measurement, and comparison problems.
Key concepts
Level 1 — Decimal place value ↔ fraction
Verbal: The name of the place tells the denominator — tenths → 10, hundredths → 100.
Symbolic:
| Decimal | Fraction | Reason |
|---|---|---|
| 0.7 | 7/10 | 7 tenths |
| 0.25 | 25/100 = 1/4 | 25 hundredths |
| 2.5 | 2 + 5/10 = 5/2 | mixed number |
Visual: Shade 3 columns of a 10×10 grid → 0.03 = 3/100.
Level 2 — Division method and comparison
Fraction → decimal: Divide numerator by denominator. 3/8 = 3 ÷ 8 = 0.375.
Common equivalents to memorise:
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
Compare: Convert to same form — 0.6 vs 2/3 → 0.6 vs 0.666… so 2/3 is larger.
Money link: ₹1.50 = ₹1 + 50/100 = ₹3/2 as improper rupee fraction in problems.
Worked example
Convert 5/8 to a decimal and 0.375 to a fraction in lowest terms.
Part A — 5 ÷ 8:
5.000 ÷ 8 = 0.625
Part B — 0.375 = 375/1000
HCF(375, 1000) = 125
375/1000 = 3/8 ✓ (same fraction!)
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| 1/3 = 0.3 exactly | Rounding too early | 1/3 = 0.333… (repeating); use fraction for exact value |
| 0.5 = 1/50 | Reading decimal as two separate digits | 0.5 = 5/10 = 1/2 |
| Not simplifying 50/100 | Stopping at place-value fraction | Always reduce: 50/100 = 1/2 |
| Comparing without converting | Eye-balling | Pick one form (both decimals or both fractions) |
Quick check
- Write 0.08 as a fraction in lowest terms.
- Convert 7/20 to a decimal.
- Which is greater: 0.45 or 4/9? Show your method.
- Express ₹2.75 as a mixed number of rupees.
Open the Practice tab for graded questions on Fraction–Decimal Conversions.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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