Converting Percents, Decimals, and Fractions
Practice fast, accurate conversions among all three number forms to improve problem-solving flexibility.
Data comes at you in all three forms at once: a loan rate is 6.5%, a material waste factor is \(\frac{3}{20}\), and a profit margin is 0.18. The professional who can translate between these instantly — without hunting for a calculator — moves faster, makes fewer errors, and earns more trust. Mastering all six conversion paths is a foundational business math skill.
- Apply all six conversion rules (Percent↔Decimal, Percent↔Fraction, Decimal↔Fraction)
- Choose the fastest conversion path for any given starting form
- Recognize when to round and when to express results exactly
There are three number forms — Percent, Decimal, Fraction — and six conversion paths between them. Each path has one simple rule:
- % → Decimal: divide by 100 (÷ 100)
- Decimal → %: multiply by 100 (× 100)
- % → Fraction: write over 100, simplify
- Fraction → %: divide top ÷ bottom, then × 100
- Decimal → Fraction: read place value, write over power of 10, simplify
- Fraction → Decimal: divide top ÷ bottom
A fast shortcut: convert everything to decimal first (easiest step), then to the target form.
All Six Conversion Rules at a Glance
Conversion Reference Table
| From → To | Rule | Example |
|---|---|---|
| % → Decimal | ÷ 100 | 48% → 0.48 |
| Decimal → % | × 100 | 0.73 → 73% |
| % → Fraction | Write over 100, simplify | 60% → \(\frac{60}{100}\) = \(\frac{3}{5}\) |
| Fraction → % | Divide top ÷ bottom × 100 | \(\frac{3}{8}\) → 0.375 → 37.5% |
| Decimal → Fraction | Place value over power of 10, simplify | 0.6 → \(\frac{6}{10}\) = \(\frac{3}{5}\) |
| Fraction → Decimal | Divide top ÷ bottom | \(\frac{5}{8}\) → 0.625 |
Convert 80% to decimal and fraction.
- 80% ÷ 100 = 0.80
- \(\frac{80}{100}\), GCF=20 → \(\frac{4}{5}\)
Convert \(\frac{7}{20}\) to decimal and percent.
- Decimal: 7 ÷ 20 = 0.35.
- Percent: 0.35 × 100 = 35%.
Financial analyst Rosa is reviewing a quarterly report. Three KPIs are listed in different forms: conversion rate = \(\frac{3}{16}\), gross margin = 0.22, customer satisfaction = 87%. She needs all three as percents to compare them on the same chart.
- \(\frac{3}{16}\): 3 ÷ 16 = 0.1875 → 18.75%
- 0.22 × 100 = 22%
- 87% → already done: 87%
Rosa's chart shows: Conversion 18.75% | Margin 22% | Satisfaction 87% — three clean, comparable values.
Test yourself:
- Convert 0.125 to a percent and a fraction.
- Convert \(\frac{9}{25}\) to decimal and percent.
- Convert 45% to a fraction in simplest form.
▶ Show Answers
- 0.125 × 100 = 12.5%; 0.125 = \(\frac{125}{1000}\). GCF=125 → \(\frac{1}{8}\).
- 9 ÷ 25 = 0.36; 0.36 × 100 = 36%.
- \(\frac{45}{100}\). GCF=5 → \(\frac{9}{20}\).
- Moving the decimal the wrong direction: ❌ 35% → decimal = 35.0. ✅ Divide by 100: 35% = 0.35. The decimal moves LEFT when going from percent to decimal.
- Skipping simplification: \(\frac{60}{100}\) is technically correct but never leave it unsimplified — the expected answer is \(\frac{3}{5}\).
- Rounding repeating decimals too soon in multi-step problems: Keep full precision (\(0.\overline{3}\)) until the final step to avoid accumulated rounding error.
- Six paths, six rules — each has a single, consistent operation to apply.
- Decimal is the bridge — convert to decimal first, then to either percent or fraction.
- Always simplify fractions after converting from percent or decimal form.
- Exact vs. approximate: use \(\frac{1}{3}\) or \(0.\overline{3}\) when precision matters; use 33.3% only for estimation.
Business analysts and accountants receive data in all three forms simultaneously — from different systems, departments, and countries. A profit margin of 0.18, a tax rate of 18%, and a cost ratio of \(\frac{9}{50}\) are all the same number. Recognizing this instantly — and converting without effort — is a fundamental professional competency in any analytical role.
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Converting Percents, Decimals, and Fractions — Quiz
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