How to Convert Fractions to Decimals and Percents

Fractions, decimals, and percents are three ways of writing the same amount. Homework often asks you to move between them, and most mistakes come from skipping a step or misplacing a decimal point. This guide walks through each conversion with worked examples, then shows how to check your answer.

1. The one idea that connects all three

A percent is a rate per 100. The Common Core grade 6 standards put it plainly: 30% of a quantity means 30/100 times the quantity. So "percent" is really a fraction with a denominator of 100, written in a shorter way.

A decimal is also a fraction in disguise. The digits after the decimal point stand for tenths, hundredths, thousandths, and so on. Once you see that, every conversion becomes a question of rewriting the same number.

2. Fraction to decimal: divide the top by the bottom

The grade 7 standards describe the method directly: convert a rational number to a decimal using long division. The fraction bar means "divided by."

Example 1: 3/8

Divide 3 by 8. Since 8 does not go into 3, write 3 as 3.000 and keep dividing.

• 8 goes into 30 three times (24), remainder 6.
• 8 goes into 60 seven times (56), remainder 4.
• 8 goes into 40 five times (40), remainder 0.

So 3/8 = 0.375. The division ended with a remainder of 0, so this decimal stops, or terminates.

Example 2: 2/3

Divide 2 by 3. 3 goes into 20 six times (18), remainder 2. Then 3 goes into 20 six times again, remainder 2, and the same step repeats forever.

So 2/3 = 0.666..., often written with a bar over the 6. The same grade 7 standard states that the decimal form of a rational number either terminates in 0s or eventually repeats. That gives you a built-in check: if your long division never ends and never repeats, you have made an arithmetic slip.

3. A shortcut when the denominator fits into 100

If you can multiply the denominator to reach 10, 100, or 1,000, you can skip long division.

Example 3: 7/20

20 times 5 is 100, so multiply the top and bottom by 5: 7/20 = 35/100 = 0.35.

This works for denominators like 2, 4, 5, 10, 20, 25, and 50. A useful pattern: after simplifying, a fraction terminates when its denominator has no prime factors other than 2 and 5. A denominator of 3, 6, 7, 9, or 11 will give a repeating decimal.

4. Decimal to percent: move two places

Since percent means "per 100," multiply the decimal by 100. That moves the decimal point two places to the right.

Fraction	Decimal	Percent
3/8	0.375	37.5%
7/20	0.35	35%
2/3	0.666...	about 66.7%
1/6	0.1666...	about 16.7%
5/4	1.25	125%

Two details are worth noticing. First, a repeating decimal gives a percent you have to round, so write "about" or follow the rounding your teacher asks for. Second, a fraction bigger than 1, like 5/4, gives a percent bigger than 100. That is not an error. It just means more than the whole.

5. Percent back to fraction

Write the percent over 100, then simplify.

Example 4: 45%

45% = 45/100. Both numbers divide by 5, giving 9/20.

Example 5: 37.5%

37.5% = 37.5/100. Multiply the top and bottom by 10 to clear the decimal: 375/1,000. Divide both by 125 to get 3/8, which matches Example 1.

6. Using percents in word problems

The grade 6 standards list two problem types: finding a percent of a quantity, and finding the whole when you know a part and the percent.

Percent of a quantity: What is 30% of 80? Write 30% as 0.30 and multiply: 0.30 x 80 = 24.

Finding the whole: 12 is 15% of what number? Here 12 is the part. Write the equation 0.15 x (whole) = 12, then divide: 12 / 0.15 = 80. Check it: 15% of 80 is 0.15 x 80 = 12, which matches.

7. Common mistakes

• Dividing the wrong way. 3/8 means 3 divided by 8, not 8 divided by 3. If your decimal for a fraction smaller than 1 comes out bigger than 1, flip the division.
• Moving the decimal the wrong direction. Going from decimal to percent, the number should get bigger (0.35 becomes 35). Going from percent to decimal, it should get smaller.
• Reading 0.5% as 50%. 0.5% is half of one percent, which is 0.005 as a decimal. Write the percent over 100 if you are unsure: 0.5/100 = 0.005.
• Rounding too early. If a problem has several steps, keep the full fraction (like 2/3) until the end, and round only the final answer.

8. How to check any conversion

Convert back. If 3/8 became 37.5%, turn 37.5% back into a fraction and see whether you land on 3/8 again, as in Example 5. You can also estimate: 3/8 is a bit less than 1/2, so the percent should be a bit less than 50%. An answer of 3.75% or 375% fails that quick test right away.

9. Key takeaways

• A percent is a rate per 100, so any percent can be written as a fraction over 100.
• To turn a fraction into a decimal, divide the numerator by the denominator using long division.
• Every fraction gives a decimal that either stops or eventually repeats, which is a handy check on your division.
• To go from decimal to percent, multiply by 100; to go back, divide by 100.
• Check every conversion by converting back and by estimating whether the size of the answer makes sense.