A 25%-off sale tag is just the fraction 1/4 wearing different clothes, because every percent is a fraction with 100 hiding underneath. Converting means dividing the top number by the bottom number and then multiplying by 100, which is the same as sliding the decimal point two places to the right. One quarter becomes 0.25, and 0.25 becomes 25%. Seventeen out of twenty on a quiz becomes 0.85, then 85%. Shoppers reading discount signs, students turning test scores into grades, and managers reporting growth figures all speak percent because it puts every fraction on the same 100-point scale. Comparing 85% to 90% is effortless; comparing 17/20 to 9/10 takes a beat longer.

The two-step method, done once slowly.

Step one is division: the fraction bar is a division sign in disguise. For 3/4, divide 3 by 4 to get 0.75. Step two is multiplication by 100: 0.75 times 100 is 75, and the percent sign goes on the end. That is the whole method, and it never changes: divide, multiply by 100, add the sign. The page's own example, 3 over 4, gives 75%, and its decimal readout shows 0.75 beside it so you can see both forms at once. Reversing the trip is just as mechanical: to turn a percent back into a fraction, write it over 100 and simplify. 25% is 25 over 100, which simplifies to 1/4. 12.5% is 12.5 over 100, which is 125 over 1000, which simplifies to 1/8. 75% is 75 over 100, which is 3/4. Every percent you meet is a fraction waiting to be reduced.

The ladder worth memorizing.

Halves, quarters, fifths, and eighths cover most of daily life. One half is 50%, one quarter is 25%, three quarters is 75%. One fifth is 20%, two fifths is 40%, three fifths is 60%, four fifths is 80%. One eighth is 12.5%, three eighths is 37.5%, five eighths is 62.5%, seven eighths is 87.5%. Tenths are trivial: 1/10 is 10%, 3/10 is 30%, 7/10 is 70%. Twentieths show up on quizzes: 17/20 is 85%, 18/20 is 90%, 19/20 is 95%. Twenty-fifths are nearly as friendly: 13/25 is 52%, because 13 times 4 is 52 and 25 times 4 is 100. Learn the eighths and the fifths and you will rarely need the calculator for a price tag or a test score, because most real-world fractions are built from them.

Repeating decimals and the 2-and-5 rule.

Not every fraction lands cleanly. One third is 0.333 repeating, which becomes 33.333 repeating percent, usually written as 33.33% or as 33 and 1/3%. Two thirds is 66.666 repeating percent, rounded to 66.67%. One sixth is 16.666 repeating percent, rounded to 16.67%. One seventh is about 14.29%, one ninth is about 11.11%, and one eleventh is about 9.09%. The rule behind the mess: a fraction terminates only when its denominator, after simplifying, has no prime factors other than 2 and 5. Denominators like 4, 8, 20, and 25 terminate; denominators containing 3, 6, 7, 9, or 11 repeat forever. That is why 5/8 is a clean 62.5% while 5/6 is a repeating 83.33%. For repeating results, decide the precision before you round: money usually wants two decimals, 66.67%, while a classroom answer may want the exact fraction form, 66 and 2/3%. Never round in the middle of a multi-step calculation, or the error rides along into the final answer.

Mixed numbers and percents above 100.

A mixed number converts the same way, and the result passes 100%, which surprises people exactly once. One and three quarters is 7/4: 7 divided by 4 is 1.75, times 100 is 175%. Two and one half is 5/2, which is 250%. A fraction larger than 1 always gives a percent larger than 100, because the part is bigger than the whole: 5/4 is 125%, which is how you describe a price that rose by a quarter, or a team that scored 25% more than its target. The reverse trip works too: 125% is 125 over 100, which simplifies to 5/4. Students sometimes insist a percent cannot pass 100, but interest, growth rates, and performance bonuses do it routinely: a 150% return means you got your money back plus half again.

Simplify first, convert second.

Simplifying before dividing makes the arithmetic smaller and the repeating-decimal question clearer. 50/100 simplifies to 1/2, which is 50%, with no long division at all. 12/16 simplifies to 3/4, which is 75%. 18/24 simplifies to 3/4 as well, which is the fastest way to see that 18/24 and 3/4 are the same grade. Simplification also exposes the termination rule: 6/15 looks like it might repeat, but it simplifies to 2/5, which is a clean 40%. The calculator does not require simplified input, it divides whatever you type, but the habit saves time and catches the case where two different-looking fractions are secretly the same score.

Test scores, discounts, and the real world.

Grades are the most common conversion in American life. A quiz score of 17 out of 20 is 85%, a solid B. A score of 23 out of 25 is 92%, an A. A score of 41 out of 50 is 82%, a B-minus on most scales. Teachers convert because a percent travels across quizzes of different lengths: 17/20 and 34/40 are both 85%, and the percent makes that obvious. Discounts work the same way in reverse: a quarter off a price is 25% off, so an 80-dollar jacket at a quarter off costs 60 dollars, saving 20. A store advertising 3/8 off is advertising 37.5% off, which is why the percent sign dominates sale tags: 37.5% reads instantly, while 3/8 off takes a second of thought. Polls, tips, tax rates, and batting averages are all fractions dressed as percents, and the conversion is identical every time.

The rounding trap with thirds.

Three thirds make a whole, but three rounded thirds do not: 33.33% plus 33.33% plus 33.33% is 99.99%, not 100%. The missing 0.01% is rounding error, not a mystery, and it appears whenever rounded percents are added back together. Election results, survey breakdowns, and budget shares that sum to 99.9% or 100.1% are showing the same effect. The fix is to keep the exact fractions until the final step, or to note that one entry carries the rounding remainder: report 33.33%, 33.33%, and 33.34% if the total must read 100%. The same caution applies to the calculator's own precision: its Percentage readout shows 4 decimals, so 2/3 reads 66.6667%, and rounding that to 66.67% for a price tag is correct, while rounding it to 67% for a lab report may not be.

How to use the calculator above.

Type the top number into the Numerator box and the bottom number into the Denominator box, then read the Percentage result with the Decimal readout beside it. Try 17 and 20 for 85%, try 1 and 3 for 33.3333%, try 5 and 8 for 62.5%, and try 8 and 13 for about 61.5385%, a repeating-style result from a denominator with a factor of 13. The denominator cannot be zero: division by zero is undefined, and no percent exists for it. For a mixed number, convert the whole part separately: 1 and 3/4 is 100% plus 75%, which is 175%, or convert the improper fraction 7/4 directly.

Finding a percent of a number, and percentage points.

The reverse skill, finding a percent of a quantity, uses the same division in the other direction: turn the percent into a decimal and multiply. Twenty percent of 250 is 0.20 times 250, which is 50. A 15% tip on a 60-dollar meal is 0.15 times 60, which is 9 dollars. A 7.5% sales tax on an 80-dollar purchase is 0.075 times 80, which is 6 dollars. Thirty percent off a 120-dollar coat saves 36 dollars and leaves a price of 84. The pattern is always the same: percent to decimal by dividing by 100, then multiply. Related but different is the percentage point: when a mortgage rate rises from 6% to 7%, that is a rise of 1 percentage point, but a relative rise of 1 divided by 6, which is 16.67%. News reports that confuse the two make a 1-point rise sound like a 1% rise, understating it sixteenfold. Keep the units straight: percentage points measure the arithmetic gap, percent measures the proportional gap.

Mistakes to avoid.

The most common error is stopping at the decimal: 3/4 is 0.75, not 0.75%, and writing 0.75% means less than one percent, a hundredfold mistake. The second is dividing backwards: 4 divided by 3 is 133.33%, which is the reciprocal's percent, not 3/4's 75%. The third is forgetting that the percent sign already means divided by 100: 50% is 50 over 100, not 50 over 100 over 100 again. The fourth is rounding a repeating decimal too early and then multiplying: 1/3 rounded to 0.33, times 100, gives 33%, but the true value is 33.33%, and across a thousand-unit order that 0.33% is real money. And the fifth is treating a percent like a plain number in addition: 25% off followed by 25% off is not 50% off, because the second discount applies to the already-reduced price. Divide, multiply by 100, add the sign, and check the direction, and the conversion takes care of itself.

With the pre-filled defaults — Numerator 3, Denominator 4 — the Fraction to Percent returns Percentage 75.0000%, Decimal 0.75000000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.