Ask most students to convert 3/5 or 7/20 into a decimal, and they will immediately draw a long division bracket, place a decimal point, add trailing zeros, and slog through vertical subtraction. But decimal numbers are literally named after decem, the Latin word for ten. If you can rescale the denominator into 10, 100, or 1,000, you can read off the decimal answer instantly with zero division required.
The Friendly Denominators Law
Look for denominators that multiply cleanly into 10, 100, or 1,000:
- 2: Multiply by 5 to make 10.
- 4: Multiply by 25 to make 100.
- 5: Multiply by 2 to make 10 (or by 20 to make 100).
- 8: Multiply by 125 to make 1,000.
- 20: Multiply by 5 to make 100.
- 25: Multiply by 4 to make 100.
- 50: Multiply by 2 to make 100.
Step-by-Step Conversion Walkthroughs
Example 1: Convert 3/5 to a Decimal
- Target: Turn denominator 5 into 10.
- Multiplier:
5 × 2 = 10. - Multiply top and bottom:
(3 × 2) / (5 × 2) = 6/10. - Say it aloud: "Six tenths." In decimal notation, that is 0.6!
Example 2: Convert 7/20 to a Decimal
- Target: Turn 20 into 100.
- Multiplier:
20 × 5 = 100. - Multiply top and bottom:
(7 × 5) / (20 × 5) = 35/100. - Say it aloud: "Thirty-five hundredths." In decimal notation: 0.35!
Example 3: Convert 13/25 to a Decimal
- Multiply by 4:
(13 × 4) / (25 × 4) = 52/100. - Written as decimal: 0.52!
Example 4: Convert 3/8 to a Decimal
- 8 multiplies by 125 to make 1,000.
3 × 125 = 375.375 / 1,000 = 0.375(Three hundred seventy-five thousandths).
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Frequently Asked Questions
Any fraction whose denominator has prime factors of only 2 and/or 5 can be converted easily (e.g., 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 125). These denominators divide evenly into powers of 10.
Denominators with prime factors other than 2 or 5 produce repeating decimals. For these, memorize benchmark fractions (1/3 = 0.333..., 2/3 = 0.666..., 1/6 = 0.1666..., 1/9 = 0.111...) or use short division.
Comparing decimals is trivial because place values align directly. If you convert 3/5 to 0.60 and 5/8 to 0.625, you immediately see that 5/8 is larger.