Fraction ↔ Decimal ↔ Percent Conversion

Why This Matters for Nursing: Lab results might show 0.45, medication strengths as 1/4, or infection rates as 15%. Being fluent in all three formats helps you communicate with doctors, patients, and pharmacists.

What You Need to Know

Fractions, decimals, and percents are three ways to express the SAME value:

Percent literally means "per hundred" — so 50% = 50/100 = 0.50

🧠 Memory Trick

Fraction → Decimal: "Divide the top by the bottom" (numerator ÷ denominator)

Decimal → Percent: "Move decimal 2 places RIGHT and add %" (multiply by 100)

Percent → Decimal: "Move decimal 2 places LEFT and drop %" (divide by 100)

Think: "Percent is always the biggest looking number" — 0.5 → 50% (decimal moves right to get bigger)

Conversion Methods

Fraction → Decimal

Divide the numerator by the denominator

3/4 → 3 ÷ 4 = 0.75

Decimal → Fraction

1. Write the decimal over its place value
2. Simplify

0.75 = 75/100 = 3/4

Decimal → Percent

Multiply by 100 (or move decimal 2 places RIGHT)

0.75 → 75%

Percent → Decimal

Divide by 100 (or move decimal 2 places LEFT)

75% → 0.75

Fraction → Percent

Convert to decimal first, then to percent

3/4 → 0.75 → 75%

Percent → Fraction

Write over 100, then simplify

75% = 75/100 = 3/4

✏️ Worked Examples

Example 1: Fraction to Decimal

Problem: Convert 5/8 to a decimal.

Step 1 — Set up the division. The fraction 5/8 literally means "5 divided by 8." The numerator (top number) goes inside the division bracket; the denominator (bottom number) goes outside.

Step 2 — Divide 5 by 8. 8 doesn't go into 5, so add a decimal point and zeros: 8 goes into 50 six times (6 × 8 = 48), remainder 2. Then 8 goes into 20 twice (2 × 8 = 16), remainder 4. Then 8 goes into 40 five times (5 × 8 = 40), remainder 0. Done!

Answer: 0.625

💡 Shortcut: Memorize 1/8 = 0.125. Then 5/8 = 5 × 0.125 = 0.625. Memorizing common fractions saves time on the TEAS.