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§ Fractions

Fraction / Decimal / Percent

§ Fractions

Fraction / Decimal / Percent

CCSS.6.RPCCSS.7.NS3 min read

Fractions, decimals, and percentages represent identical mathematical values in different formats. The fraction 3/4 equals the decimal 0.75, which equals 75 percent. Converting between these forms requires understanding that fractions represent division, decimals show place value positions, and percentages express parts per 100.

§ 01

Why it matters

Converting between fractions, decimals, and percentages appears throughout daily life and advanced mathematics. Store discounts show percentages like 25% off, which equals 0.25 or 14 of the original price. Scientific measurements often use decimals like 0.375 liters, while recipes call for fractional amounts like 38 cup. Sports statistics combine all three formats — a batting average of 0.300 equals 30% or 310. In algebra and statistics, students must fluently convert between these forms to solve equations and interpret data. Financial calculations require percentage-to-decimal conversions for interest rates, while engineering uses fractional measurements that convert to decimal equivalents for precision calculations.

§ 02

How to solve fraction / decimal / percent

Fraction / Decimal / Percent

  • Fraction → decimal: divide numerator by denominator.
  • Decimal → percent: multiply by 100.
  • Percent → fraction: write over 100, simplify.

Example: 38 → 0.375 → 37.5%.

§ 03

Worked examples

Beginner§ 01

Convert 14 to a decimal.

Answer: 0.25

  1. Divide numerator by denominator → 1 ÷ 4 = 0.25 — Fraction means division.
  2. Verify → 14 = 0.25 ✓ — Check.
Easy§ 02

Convert 310 to a decimal.

Answer: 0.3

  1. Divide numerator by denominator → 3 ÷ 10 = 0.3 — Fraction means division.
  2. Verify → 310 = 0.3 ✓ — Check.
Medium§ 03

Convert 0.4545 to a percent.

Answer: 45.45%

  1. Multiply by 100 → 0.4545 × 100 = 45.45% — Move the decimal point two places right.
  2. Verify → 45.45% ✓ — Check.
§ 04

Common mistakes

  • Converting 3/4 to 0.34 instead of 0.75 by placing numerator and denominator side by side rather than dividing.
  • Writing 0.6 as 6% instead of 60% by forgetting to multiply by 100 when converting decimal to percentage.
  • Converting 25% to 1/25 instead of 1/4 by using the percentage number as the denominator rather than placing it over 100 and simplifying.
§ 05

Frequently asked questions

How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 5/8 becomes 5 ÷ 8 = 0.625. This works because fractions represent division operations that can be completed using long division or a calculator.
What's the quickest way to convert decimals to percentages?
Multiply by 100 and add the percent symbol. The decimal 0.73 becomes 0.73 × 100 = 73%. This shifts the decimal point two places to the right because 100 has two zeros.
How do you turn a percentage into a fraction?
Place the percentage number over 100 and simplify. For instance, 40% becomes 40/100, which reduces to 2/5 by dividing both numerator and denominator by their greatest common factor of 20.
Which decimals create repeating patterns?
Fractions with denominators containing prime factors other than 2 and 5 produce repeating decimals. Examples include 1/3 = 0.333... and 2/7 = 0.285714285714... where the digits cycle indefinitely.
What are the most important benchmark conversions to memorize?
Key conversions include 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, and 1/10 = 0.1 = 10%. These appear frequently in mathematics and real-world applications.
§ 06

See also

FractionPercentageNumeratorDenominatorFactor
§ 06

Related topics

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