3.4 Converting Percentage ↔︎ Fraction ↔︎ Decimal

Percentage to fraction: Write the percentage over 100 and simplify. 37.5% = (37.5)/(100) = (375)/(1000) = (3)/(8)

Fraction to percentage: Multiply the fraction by 100, or use the table above if it’s a common one. (5)/(8) × 100 = 62.5% (also: 1/8=12.5%, so 5/8 = 5× 12.5% = 62.5%)

Decimal to percentage: Multiply by 100 (shift the decimal point two places right). 0.045 × 100 = 4.5%

Percentage to decimal: Divide by 100 (shift the decimal point two places left). 6% = 0.06.

Worked Example 1: Convert 5/6 into a percentage. Since 1/6 = 16.67%, 5/6 = 5 × 16.67% = 83.33%.

Worked Example 2: What fraction is 62.5%? 62.5/100 = 625/1000 = 5/8.

Worked Example 3: A survey shows 0.375 of respondents prefer tea. Express this as a percentage. 0.375 × 100 = 37.5%.

Worked Example 4: Express 4 3/4 as a percentage, and separately express 8.5% as a fraction in lowest terms. 4 3/4 = 4.75; as a percentage this is 4.75 × 100 = 475% (percentages greater than 100% are common when comparing a larger quantity to a smaller base, e.g., “this year’s profit is 475% of last year’s profit”). 8.5% = 8.5/100 = 85/1000 = 17/200 in lowest terms.

Worked Example 5: Convert 2 5/8 into a percentage, and separately convert 133 1/3% into a fraction in lowest terms. 2 5/8 = 2.625; as a percentage this is 2.625 × 100 = 262.5%. 133 1/3% = (400/3)/100 = 400/300 = 4/3 (check: 4/3 = 1.3333 = 133.33%, confirmed).

Worked Example 6: Express 5/32 as a percentage, and express 8.75% as a fraction in lowest terms. 5/32 = 0.15625; × 100 = 15.625% (5/32 does not fall in the standard 1/n table, so long division is unavoidable here — this is exactly why the table only goes up to 1/20). 8.75% = 8.75/100 = 875/10000. Dividing numerator and denominator by 125 gives 7/80 (check: 7/80 = 0.0875 = 8.75%, confirmed).