Fractions, Decimals and Percentages: How to Convert Between Them

Three quarters, 0.75 and 75% are the same number written three ways. Each form is suited to a different job. Fractions are exact and easy to scale, decimals are easy to compare and type into a calculator, and percentages make shares of different totals comparable. Being able to move between them quickly makes discounts, recipes, test scores and measurements much less of a chore. This guide covers each conversion, the cases that cause trouble, and a reference table of common values.

One number, three forms

A fraction such as 3/4 means 3 divided by 4. Doing that division gives the decimal, 0.75. A percentage is a decimal scaled to “per hundred”, so 0.75 becomes 75%. Every conversion in this guide follows from those two facts:

• Fraction → decimal: divide the numerator by the denominator.
• Decimal → percentage: multiply by 100, which moves the decimal point two places right.

The reverse conversions undo those steps.

Fraction to decimal

Divide the top number by the bottom number. For 5/8, that’s 5 ÷ 8 = 0.625. Long division works if you don’t have a calculator: 8 doesn’t go into 5, so write 0. and bring down a zero to make 50. 8 goes into 50 six times (48), leaving 2. Bring down another zero to get 20, which takes 8 twice (16), leaving 4. Then 40 takes 8 exactly five times. The digits are 6, 2 and 5, so 5/8 = 0.625.

Sometimes the division never ends. 7/12 gives 0.58333…, with the 3 repeating forever. That’s not an error; it’s simply a number that can’t be written exactly as a finite decimal. When you write it down, you round it, which is why the fraction is the more precise form.

Which fractions give repeating decimals?

Simplify the fraction first, then look at the prime factors of the denominator. If the only prime factors are 2 and 5, the decimal terminates. If any other prime appears, the decimal repeats.

• 3/40 terminates (40 = 2 × 2 × 2 × 5): it’s 0.075.
• 1/6 repeats (6 = 2 × 3): it’s 0.1666…
• 3/15 looks like it might repeat, but it simplifies to 1/5, which is 0.2.

This is because our number system is based on 10, and 10 = 2 × 5. Only fractions that can be rewritten over 10, 100, 1,000 and so on have finite decimals.

Decimal to percentage and back

Multiply a decimal by 100 to get a percentage: 0.375 is 37.5%, 2.5 is 250%, and 0.045 is 4.5%. To go the other way, divide by 100: 62% is 0.62 and 0.5% is 0.005.

The second one is a frequent slip. Half a percent is 0.005, not 0.5. Interest rates and fees are often small percentages, so it’s worth double-checking the number of zeros. A 0.5% fee on $2,000 is $10, while multiplying by 0.5 by mistake would give $1,000.

Percentage to fraction

Write the percentage over 100 and simplify.

• 35% = 35/100. Both numbers divide by 5, giving 7/20.
• 12.5% = 12.5/100. Multiply top and bottom by 10 to clear the decimal, giving 125/1000, which simplifies to 1/8.
• 150% = 150/100 = 3/2, or 1 1/2.

The fraction calculator can do the simplifying step for you. Enter the fraction you’ve written over 100 and multiply it by 1/1 to get lowest terms.

Decimal to fraction

Terminating decimals

Count the digits after the decimal point. Write the decimal digits over 1 followed by that many zeros, then simplify. 0.84 has two decimal places, so it’s 84/100. The greatest common divisor of 84 and 100 is 4, so 0.84 = 21/25. Likewise 0.65 = 65/100 = 13/20.

Repeating decimals

A repeating decimal can always be turned back into an exact fraction. When the whole decimal part repeats, put the repeating block over the same number of 9s.

• 0.272727… has the two-digit block 27, so it’s 27/99, which simplifies to 3/11.
• 0.454545… is 45/99 = 5/11.
• 0.333… is 3/9 = 1/3.

When only part of the decimal repeats, use a little algebra. Let x = 0.1666…. Then 10x = 1.666… and 100x = 16.666…. Subtracting the first from the second removes the repeating tail: 90x = 15, so x = 15/90 = 1/6.

Conversion table

Decimals that repeat are shown with “…”, and their percentages are rounded to two decimal places. All other values are exact.

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333…	33.33%
2/3	0.666…	66.67%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
3/5	0.6	60%
4/5	0.8	80%
1/6	0.1666…	16.67%
5/6	0.8333…	83.33%
1/7	0.142857142857…	14.29%
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/9	0.111…	11.11%
1/10	0.1	10%
1/11	0.0909…	9.09%
1/12	0.08333…	8.33%
1/16	0.0625	6.25%
1/20	0.05	5%
1/25	0.04	4%
1/50	0.02	2%
1/100	0.01	1%

You can build many other values from this table. 3/10 is three times 1/10, so it’s 0.3 or 30%. 7/20 is seven times 1/20, so it’s 0.35 or 35%. For inch fractions in sixteenths, including millimeter equivalents, see the table on the fraction calculator page.

Choosing the right form

Use fractions when exactness matters or when you’re scaling. Recipes, construction measurements and probabilities often come out cleaner as fractions. Three people splitting a bill each pay exactly 1/3, while 0.33 of it each would leave a cent unpaid on every dollar.

Use decimals for arithmetic on a calculator, for comparing sizes, and for money. Is 5/8 or 3/5 larger? As decimals, 0.625 and 0.6, the answer is obvious.

Use percentages to compare shares of different totals. Scoring 21 out of 25 on one quiz and 34 out of 40 on another is easier to judge as 84% and 85%. Percentages are also the standard language for discounts, interest rates and tax. The percentage calculator converts any part and whole into a percentage directly.

Ratios fit into the same family. A ratio of 3 : 1 means the first part is 3/4 of the total, which is 0.75 or 75%. The ratio calculator reports the share of the total for any simplified ratio.

Common mistakes

• Treating rounded decimals as exact. 1/3 is not 0.33. Three times 0.33 is 0.99, not 1. Keep the fraction for further calculation, or carry more decimal places.
• Dropping a zero. 0.5% is 0.005 and 5% is 0.05. Read percentages aloud as “per hundred” to keep the scale straight.
• Converting the denominator only. To write 3/4 as a percentage, the whole fraction is scaled. It becomes 75/100, not 3/100.
• Forgetting to simplify. 0.84 = 84/100 is correct, but 21/25 is the form most people expect.
• Confusing percentage points with percent. Moving from 20% to 25% is a 5 percentage point rise, but a 25% increase. The percentage change calculator handles the second kind of comparison.

Quick summary

1. Fraction to decimal: divide top by bottom.
2. Decimal to percentage: multiply by 100.
3. Percentage to decimal: divide by 100.
4. Percentage to fraction: write over 100 and simplify.
5. Decimal to fraction: write over a power of 10 and simplify, or use 9s for repeating decimals.
6. Denominators made only of 2s and 5s give terminating decimals; anything else repeats.