Converting Fractions: Fractions, Decimals, and Percentages

1. Fraction to Decimal

To convert a fraction to a decimal, divide the numerator by the denominator.

Simple Example

For 3/4:

  • Divide 3 ÷ 4 = 0.75
  • Result: 3/4 = 0.75

Repeating Decimals

For 1/3:

  • 1 ÷ 3 = 0.333...
  • Written as 0.3̅

Use a calculator for complex fractions, but understanding the process builds intuition.

2. Decimal to Fraction

To convert a decimal to a fraction:

  1. Write the decimal as a fraction with a power of 10 as the denominator
  2. Simplify

Simple Example

For 0.6:

  • Write as 6/10
  • Simplify: 6/10 ÷ 2/2 = 3/5
  • Result: 0.6 = 3/5

Repeating Decimals

For 0.3̅:

  • Advanced methods confirm 0.3̅ = 1/3

3. Fraction to Percentage

A percentage is a fraction out of 100. To convert:

  1. Convert the fraction to a decimal
  2. Multiply by 100 and add the % sign

Method 1: Decimal

For 2/5:

  • 2/5 = 0.4 (2 ÷ 5)
  • 0.4 × 100 = 40%
  • Result: 2/5 = 40%

Method 2: Direct

For 2/5:

  • 2/5 = 40/100 = 40%

4. Percentage to Fraction

To convert a percentage to a fraction:

  1. Write the percentage as a fraction over 100
  2. Simplify

Example: 75%

  • Write as 75/100
  • Simplify: 75/100 ÷ 25/25 = 3/4
  • Result: 75% = 3/4

5. Decimal to Percentage

Multiply the decimal by 100 and add the % sign.

Example: 0.85

  • 0.85 × 100 = 85%
  • Result: 0.85 = 85%

6. Percentage to Decimal

Divide the percentage by 100 (move the decimal point two places left).

Example: 60%

  • 60 ÷ 100 = 0.6
  • Result: 60% = 0.6

Practice Problem

Convert:

  1. 5/8 to a decimal and percentage
  2. 0.25 to a fraction and percentage
  3. 45% to a fraction and decimal

Answers:

  1. 0.625, 62.5%
  2. 1/4, 25%
  3. 9/20, 0.45

Why It Matters

Converting forms is useful for:

  • Shopping: Comparing discounts (e.g., 1/4 off vs. 25%)
  • Data Analysis: Presenting stats as percentages or decimals
  • Recipes: Scaling ingredients (e.g., 0.5 cups vs. 1/2 cup)

What's Next?

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