To convert a fraction to decimal, divide the numerator (top number) by the denominator (bottom number). For example: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals (like 1/3 = 0.333...). To convert decimal to percentage, multiply by 100 (0.75 × 100 = 75%). These conversions are essential for math, cooking, construction, and everyday calculations.
Terminating vs. Repeating Decimals
Whether a fraction gives a clean (terminating) decimal or a repeating one depends on its denominator after the fraction is reduced. If the only prime factors of the denominator are 2 and 5, the decimal terminates: 1/8 = 0.125 and 1/20 = 0.05 are exact. If any other prime factor remains, the decimal repeats: 1/3 = 0.333…, 1/6 = 0.1666…, and 1/12 = 0.0833… The repeating digits are often marked with an overline or written with an ellipsis, and rounding (for example 2/3 ≈ 66.67%) is used for everyday work.
Frequently Asked Questions
Why does 1/3 equal 0.333... instead of a clean decimal?
Because 3 is not a factor of any power of 10, dividing 1 by 3 never ends — the remainder keeps producing another 3. This makes 1/3 a repeating decimal, written 0.333… or with a bar over the 3.
How do I turn a decimal back into a fraction?
Write the decimal over its place value, then simplify. 0.625 is 625/1000, which reduces to 5/8. For 0.05, that is 5/100, which reduces to 1/20.
Why are sixteenths useful in measurements?
Rulers and tools in the imperial system divide the inch into halves, quarters, eighths, and sixteenths. Each sixteenth equals 0.0625 inch, so the chart converts fractional marks directly to decimals for cutting and machining.