One Quantity, Three Notations
A half, 0.5 and 50 percent are the same amount written three ways. Which one you use depends on the job: fractions are exact and good for working, decimals compare and sort easily, percentages communicate.
Being able to switch quickly is more useful than preferring one, because most questions hand you the awkward form on purpose.
Fraction to Decimal
Divide the top by the bottom. Three quarters is 3 divided by 4, which is 0.75. That is the whole method, and it always works.
Some divisions never finish. A third is 0.3333 recurring, and a seventh runs through a six-digit cycle forever. A fraction terminates only when its denominator, once reduced, has no prime factors other than 2 and 5. That is why halves, quarters, fifths and eighths are clean and thirds and sevenths are not.
Decimal to Fraction
Write the decimal over its place value, then reduce. 0.35 is 35 over 100, which reduces to 7 over 20.
Recurring decimals need algebra rather than counting places. For 0.777 recurring, call it x, multiply by ten to get 7.777 recurring, subtract the original to leave 9x equal to 7, so x is seven ninths.
The Percentage Step
Percent means per hundred, so a percentage is a decimal multiplied by a hundred, and a decimal is a percentage divided by a hundred. 0.42 is 42 percent. Done in either direction it is a decimal point moving two places, which is why it is the easiest of the three conversions.
Worth Memorising
A handful of conversions appear so often that recalling them beats calculating them: a half is 0.5 or 50 percent, a quarter is 0.25 or 25 percent, a fifth is 0.2 or 20 percent, an eighth is 0.125 or 12.5 percent, and a third is 0.333 or 33.3 percent.
Knowing those lets you sanity-check an answer instantly. If a calculation claims three eighths is 0.6, the stored fact that an eighth is 0.125 tells you it is wrong before you redo anything.
