converting percent to fraction

Converting Percent to Fraction

Understanding Percentages

  • Definition: A percent is a representation of a number as a fraction of 100.

    • This implies that when converting a percent to a fraction, the denominator will always be 100.

Basic Conversion Process

  • Numerator and Denominator:

    • Numerator: The percent value itself.

    • Denominator: Always 100.

    • Example: 35% is expressed as:

    • 35100\frac{35}{100}

    • Interpretation: 35% equals 35 hundredths.

Converting Percentages with Decimals

  • When a percent has a decimal point, perform the following steps:

    1. Place Over 100: Start with the percent value over 100.

    2. Remove Decimal: Move the decimal point in the numerator to the right to eliminate it.

    3. Add Zeros: For each place the decimal is moved, add a zero to the denominator.

    • Example: For 68.5%:

    • Step 1: Express as 68.5100\frac{68.5}{100}

    • Step 2: Move the decimal one space to the right, resulting in 685.

    • Step 3: Add one zero to the denominator, resulting in:

      • 6851000\frac{685}{1000}

    • Interpretation: 68.5% equals 685 thousandths.

Converting Percentages Greater than 100

  • If a percent exceeds 100:

    • Use 100 as Denominator: Maintain 100 in the denominator.

    • Example: For 120%:

    • Step 1: Express as 120100\frac{120}{100}

    • This forms an improper fraction.

    • Step 2: Convert to a mixed number:

      • Change 120100\frac{120}{100} to 1 and 20/100.

    • Step 3: Simplify the fraction:

      • Reducing 20100\frac{20}{100} to 15\frac{1}{5} gives:

      • Final result: 1 and 15\frac{1}{5}