Number foundations · Topic 5 of 15

Converting Fractions, Decimals & Percents

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Math · conversions

Fraction to decimal: divide. Decimal to percent: point two places right. Percent to decimal: two places left. Memorize the quarter benchmarks.

01 · Fraction → decimalFraction → decimal: top ÷ bottom

02 · Decimal → percentDecimal → percent: point 2 places right

03 · Memorize1/4 = 25%, 1/2 = 50%, 3/4 = 75%

Fraction → decimal: numerator ÷ denominator must know

Decimal → percent: × 100 (point 2 places right), add % must know

Percent → decimal: ÷ 100 (point 2 places left), drop % must know

Percent → fraction: put it over 100, then simplify must know

Decimal → fraction: digits over the last place value, then simplify

Fraction → percent: divide to a decimal, then × 100

1/4 = 0.25 = 25% · 1/2 = 0.5 = 50% · 3/4 = 0.75 = 75% must know

1/10 = 0.1 = 10% · 1/5 = 0.2 = 20% (2/5 = 40%, 3/5 = 60%)

1/8 = 0.125 = 12.5% · 3/8 = 37.5% · 5/8 = 62.5%

1/3 = 0.333… = 33⅓% · 2/3 = 0.666… = 66⅔%

7/8 = 7 ÷ 8 = 0.875 = 87.5%

45% = 0.45 = 45/100 = 9/20

58% (0.580) < 0.6 (0.600) < 5/8 (0.625)

Commonly confused

0.4 = 40%, not 0.4% — check the direction of the move

7% = 0.07, not 0.7 (add a placeholder zero)

Ordering mixed forms: change all to decimals, then compare

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Percent = per hundred: 37% = 37/100

Repeating decimal: digits repeat forever (2/9 = 0.222…)

Over 100% → more than 1 (150% = 1.5); under 1% → < 0.01 (0.5% = 0.005)

Terminates only if the denominator’s primes are 2s and 5s

33⅓% = (100/3) ÷ 100 = 1/3

Pearl

To a percent, the point moves two places right; out of a percent, two places left.

Practice this topic, then test the whole section.

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