Percent, Fractions, and Decimal Numbers

Understanding Percent

The term percent is derived from the Latin phrase per centum, which means "per hundred." In mathematics, a percent is a ratio that compares a number to 100. This concept is fundamental in expressing proportions, comparisons, and changes in value in a standardized way.

• Percent Notation: The percent symbol (%) is used to denote a number as a fraction of 100.

• Example: 45% means 45 out of 100, or the fraction .

Converting Between Decimals, Fractions, and Percents

It is often necessary to convert between decimals, fractions, and percents. The following procedures outline the steps for these conversions:

Changing a Decimal Number to a Percent

• Step 1: Multiply the decimal number by 100. (This moves the decimal point two places to the right.)

• Step 2: Add a percent sign (%) to the result.

• Example: Convert 0.37 to a percent:

  • 0.37 × 100 = 37

  • Result: 37%

Changing a Fraction to a Percent

• Step 1: Divide the numerator (top number) by the denominator (bottom number) to obtain a decimal number.

• Step 2: Multiply the resulting decimal by 100 and add a percent sign (%).

• Example: Convert to a percent:

  • 0.6 × 100 = 60

  • Result: 60%

Changing a Percent to a Decimal or Fraction

• To Decimal: Divide the percent value by 100 and remove the percent sign.

• To Fraction: Write the percent as a fraction with a denominator of 100, then simplify if possible.

• Example: 75% as a decimal:

• Example: 75% as a fraction:

Additional info: The original notes did not complete the procedure for converting a fraction to a percent. The standard academic procedure is to first convert the fraction to a decimal, then follow the decimal-to-percent steps.