Blog · decimals

Fraction to Decimal Chart: Halves to Sixteenths, Explained

Q: How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For 3/8, 3 divided by 8 is 0.375. When the denominator can be scaled to 10, 100, 1000 or 10000, you can skip the division: 3/8 = 375/1000 = 0.375.

Q: How can I tell if a fraction makes a repeating decimal?

Simplify the fraction first, then factor the denominator. If its only prime factors are 2 and 5, the decimal terminates. Any other prime factor, such as 3, 7 or 11, makes the decimal repeat. So 3/16 terminates and 5/12 repeats, but 3/12 simplifies to 1/4 and terminates.

Q: What is 1/6 as a decimal?

1/6 is 0.1666..., written 0.16 with a bar over the 6 only. The 1 does not repeat; only the 6 does. Rounded to three places it is about 0.167.

Q: Why are sixteenths always four decimal places?

Because 16 is 2 to the fourth power, and 16 times 625 is 10000. Any sixteenth can be rewritten over 10000, so it needs at most four decimal places. For example, 7/16 = 4375/10000 = 0.4375.

October 11, 2026 · AI Math Tutor Team

A fraction to decimal chart gives you the decimal for every common fraction at a glance: $\frac{1}{2} = 0.5$ , $\frac{3}{8} = 0.375$ , $\frac{2}{3} = 0.\overline{6}$ . The chart below covers halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths, twelfths and sixteenths, with repeating decimals marked by a bar.

After the chart come the two ways to convert any fraction yourself, a quick test that tells you whether a decimal will repeat before you divide, and three worked examples.

Key takeaways

To convert a fraction to a decimal, divide the numerator by the denominator: $\frac{3}{8} = 3 \div 8 = 0.375$ .
If the denominator can be scaled to 10, 100, 1000 or 10000, scale it instead of dividing: $\frac{3}{8} = \frac{375}{1000}$ .
A simplified fraction terminates only when its denominator has no prime factors other than 2 and 5. Thirds, sixths, ninths and most twelfths repeat.
A bar marks the digits that repeat: $\frac{1}{6} = 0.1\overline{6}$ , where only the 6 repeats.

Try any fraction in the calculator below: it shows the exact decimal, marks the repeating digits, and writes out the long division.

The fraction to decimal chart

Every proper fraction for each denominator is listed, including the ones that simplify, so you can find $\frac{6}{16}$ without simplifying it first. The middle column gives the simplest form when there is a simpler one.

Halves, thirds, quarters, fifths and sixths

Fraction	Simplest form	Decimal
$\frac{1}{2}$	same	0.5
$\frac{1}{3}$	same	$0.\overline{3}$
$\frac{2}{3}$	same	$0.\overline{6}$
$\frac{1}{4}$	same	0.25
$\frac{2}{4}$	$\frac{1}{2}$	0.5
$\frac{3}{4}$	same	0.75
$\frac{1}{5}$	same	0.2
$\frac{2}{5}$	same	0.4
$\frac{3}{5}$	same	0.6
$\frac{4}{5}$	same	0.8
$\frac{1}{6}$	same	$0.1\overline{6}$
$\frac{2}{6}$	$\frac{1}{3}$	$0.\overline{3}$
$\frac{3}{6}$	$\frac{1}{2}$	0.5
$\frac{4}{6}$	$\frac{2}{3}$	$0.\overline{6}$
$\frac{5}{6}$	same	$0.8\overline{3}$

Eighths, ninths and tenths

Fraction	Simplest form	Decimal
$\frac{1}{8}$	same	0.125
$\frac{2}{8}$	$\frac{1}{4}$	0.25
$\frac{3}{8}$	same	0.375
$\frac{4}{8}$	$\frac{1}{2}$	0.5
$\frac{5}{8}$	same	0.625
$\frac{6}{8}$	$\frac{3}{4}$	0.75
$\frac{7}{8}$	same	0.875
$\frac{1}{9}$	same	$0.\overline{1}$
$\frac{2}{9}$	same	$0.\overline{2}$
$\frac{3}{9}$	$\frac{1}{3}$	$0.\overline{3}$
$\frac{4}{9}$	same	$0.\overline{4}$
$\frac{5}{9}$	same	$0.\overline{5}$
$\frac{6}{9}$	$\frac{2}{3}$	$0.\overline{6}$
$\frac{7}{9}$	same	$0.\overline{7}$
$\frac{8}{9}$	same	$0.\overline{8}$
$\frac{1}{10}$	same	0.1
$\frac{2}{10}$	$\frac{1}{5}$	0.2
$\frac{3}{10}$	same	0.3
$\frac{4}{10}$	$\frac{2}{5}$	0.4
$\frac{5}{10}$	$\frac{1}{2}$	0.5
$\frac{6}{10}$	$\frac{3}{5}$	0.6
$\frac{7}{10}$	same	0.7
$\frac{8}{10}$	$\frac{4}{5}$	0.8
$\frac{9}{10}$	same	0.9

Twelfths and sixteenths

Fraction	Simplest form	Decimal
$\frac{1}{12}$	same	$0.08\overline{3}$
$\frac{2}{12}$	$\frac{1}{6}$	$0.1\overline{6}$
$\frac{3}{12}$	$\frac{1}{4}$	0.25
$\frac{4}{12}$	$\frac{1}{3}$	$0.\overline{3}$
$\frac{5}{12}$	same	$0.41\overline{6}$
$\frac{6}{12}$	$\frac{1}{2}$	0.5
$\frac{7}{12}$	same	$0.58\overline{3}$
$\frac{8}{12}$	$\frac{2}{3}$	$0.\overline{6}$
$\frac{9}{12}$	$\frac{3}{4}$	0.75
$\frac{10}{12}$	$\frac{5}{6}$	$0.8\overline{3}$
$\frac{11}{12}$	same	$0.91\overline{6}$
$\frac{1}{16}$	same	0.0625
$\frac{2}{16}$	$\frac{1}{8}$	0.125
$\frac{3}{16}$	same	0.1875
$\frac{4}{16}$	$\frac{1}{4}$	0.25
$\frac{5}{16}$	same	0.3125
$\frac{6}{16}$	$\frac{3}{8}$	0.375
$\frac{7}{16}$	same	0.4375
$\frac{8}{16}$	$\frac{1}{2}$	0.5
$\frac{9}{16}$	same	0.5625
$\frac{10}{16}$	$\frac{5}{8}$	0.625
$\frac{11}{16}$	same	0.6875
$\frac{12}{16}$	$\frac{3}{4}$	0.75
$\frac{13}{16}$	same	0.8125
$\frac{14}{16}$	$\frac{7}{8}$	0.875
$\frac{15}{16}$	same	0.9375

Two patterns make the chart easy to rebuild. Each eighth is 0.125 more than the last, and each sixteenth is 0.0625 more. Each ninth repeats its own numerator: $\frac{4}{9} = 0.\overline{4}$ .

How to convert fractions to decimals

There are two methods. The first is faster when it works; the second always works.

Method 1: scale the denominator to a power of 10

Find a number that turns the denominator into 10, 100, 1000 or 10000. For eighths, $8 \times 125 = 1000$ . $\frac{3}{8} = \frac{3 \times 125}{8 \times 125}$
Multiply the numerator by the same number. $\frac{3 \times 125}{1000} = \frac{375}{1000}$
Read the result as a decimal: the number of zeros in the denominator is the number of decimal places. $\frac{375}{1000} = 0.375$

The scaling numbers worth remembering: $2 \times 5 = 10$ , $4 \times 25 = 100$ , $5 \times 2 = 10$ , $8 \times 125 = 1000$ , $16 \times 625 = 10000$ , $20 \times 5 = 100$ , $25 \times 4 = 100$ .

Method 2: long division

Write the numerator inside the division bracket and the denominator outside, then add a decimal point and zeros after the numerator. $5 \div 12 = 5.000\ldots \div 12$
Divide as usual, one digit at a time, bringing down a zero each time.
Stop when the remainder is 0 (the decimal terminates) or when a remainder you have already seen comes back (the digits repeat from there).

The check for either method: multiply the decimal by the denominator and you should get the numerator back. For $\frac{3}{8}$ , $0.375 \times 8 = 3$ .

How to tell if a decimal will repeat before you divide

You can predict the result before doing any division.

Simplify the fraction. $\frac{3}{12}$ becomes $\frac{1}{4}$ .
Factor the denominator into primes.
If the only primes are 2 and 5, the decimal terminates, and the number of decimal places is the larger of the two exponents. $16 = 2^4$ , so every sixteenth in simplest form has exactly 4 decimal places.
If any other prime appears, the decimal repeats. $12 = 2^2 \times 3$ , so $\frac{5}{12}$ repeats, and so do $\frac{1}{3}$ , $\frac{1}{6}$ and $\frac{1}{9}$ .

That is why step 1 matters: $\frac{3}{12}$ looks like a twelfth, but it simplifies to $\frac{1}{4} = 0.25$ , which terminates.

Repeating blocks can be long. Sevenths are not in the chart, but $\frac{1}{7} = 0.\overline{142857}$ , a block of six digits. Going the other way, a repeating decimal turns back into a fraction with a short trick: if $x = 0.\overline{3}$ , then $10x - x = 3$ , so $9x = 3$ and $x = \frac{1}{3}$ . The full method is in 0.3 Repeating as a Fraction: Why It Equals 1/3.

Worked examples

Example 1: write 7/16 inch as a decimal

The photo shows a shop worksheet question asking for the width of a 7/16 inch bolt as a decimal, taken flat under a desk lamp.

What the app read: Write $\frac{7}{16}$ as a decimal.

Check the denominator. $16 = 2^4$ , so the decimal terminates in at most 4 places. $16 = 2 \times 2 \times 2 \times 2$
Scale the denominator to 10000, because $16 \times 625 = 10000$ . $\frac{7}{16} = \frac{7 \times 625}{16 \times 625} = \frac{4375}{10000}$
Write it as a decimal with four places. $\frac{4375}{10000} = 0.4375$

So $\frac{7}{16} = 0.4375$ inch. Check: $0.4375 \times 16 = 7$ .

Example 2: write 5/12 as a decimal

The photo shows one handwritten homework problem, "5/12 as a decimal", circled in pencil on a lined page.

What the app read: Convert $\frac{5}{12}$ to a decimal.

Check the denominator. $12 = 2^2 \times 3$ , and the 3 means the decimal will repeat. $\frac{5}{12} \text{ is already in simplest form}$
Divide 5.000 by 12. 12 goes into 50 four times, remainder 2. $50 = 12 \times 4 + 2$
Bring down a zero: 12 goes into 20 once, remainder 8. $20 = 12 \times 1 + 8$
Bring down a zero: 12 goes into 80 six times, remainder 8. The remainder 8 has come back, so the 6 repeats forever. $80 = 12 \times 6 + 8$

So $\frac{5}{12} = 0.41\overline{6}$ , about 0.417. Check: $\frac{5}{12} = \frac{4}{12} + \frac{1}{12} = 0.\overline{3} + 0.08\overline{3} = 0.41\overline{6}$ .

Example 3: order 5/8, 2/3 and 3/5 from least to greatest

The photo shows a printed worksheet row with three fractions to put in order, cropped tight around that one row.

What the app read: Order from least to greatest: $\frac{5}{8}, \frac{2}{3}, \frac{3}{5}$

Convert each fraction using the chart. $\frac{5}{8} = 0.625, \quad \frac{2}{3} = 0.\overline{6}, \quad \frac{3}{5} = 0.6$
Compare the decimals digit by digit: 0.600, then 0.625, then 0.666... $0.6 < 0.625 < 0.\overline{6}$

So the order is $\frac{3}{5}, \frac{5}{8}, \frac{2}{3}$ . Check with a common denominator of 120: $\frac{72}{120} < \frac{75}{120} < \frac{80}{120}$ .

When a photo is read, the "Here's what I read" screen shows the fraction as typeset math and as editable text. Make sure $\frac{5}{12}$ was not read as 512 or $\frac{5}{2}$ before you tap "Looks right, solve it". Under the solution you can also ask for the answer as a decimal, which is a quick way to compare against your own long division.

Every post in the fraction and decimal series

Each of these answers one conversion in full, with the steps and a check:

3/8 as a Decimal: 0.375, With the Steps
0.125 as a Fraction: 1/8, Simplified Step by Step
0.375 as a Fraction: 3/8, Simplified Step by Step
1/3 as a Decimal: 0.3 repeating, With the Steps
1/8 as a Decimal: 0.125, With the Steps
3/4 as a Decimal: 0.75, With the Steps
3/16 as a Decimal: 0.1875, With the Steps
1/16 as a Decimal: 0.0625, With the Steps
2/3 as a Decimal: 0.6 repeating, With the Steps
0.625 as a Fraction: 5/8, Simplified Step by Step
1/6 as a Decimal: 0.16 repeating, With the Steps
4/5 as a Decimal: 0.8, With the Steps
5/6 as a Decimal: 0.83 repeating, With the Steps
9/16 as a Decimal: 0.5625, With the Steps
5/16 as a Decimal: 0.3125, With the Steps
7/16 as a Decimal: 0.4375, With the Steps
1/9 as a Decimal: 0.1 repeating, With the Steps
0.3 Repeating as a Fraction: Why It Equals 1/3
7/8 as a Decimal: 0.875, With the Steps
5/8 as a Decimal: 0.625, With the Steps
Reference charts: Fraction Chart: Equivalent Fractions From Halves to Twelfths, Decimal to Fraction Chart: Common Decimals as Fractions and Inch Fraction Chart: Sixteenths of an Inch as Decimals

For a general routine that works on any problem, not only conversions, see How to Solve Any Math Problem Step by Step.

Common mistakes

Dividing the wrong way. $\frac{3}{8}$ is $3 \div 8 = 0.375$ , not $8 \div 3$ . The numerator always goes inside the division bracket.
Putting the bar over too many digits. $\frac{1}{6} = 0.1\overline{6}$ , but $0.\overline{16}$ means 0.161616..., which is $\frac{16}{99}$ , a different number.
Judging a fraction before simplifying it. $\frac{3}{12}$ terminates because it equals $\frac{1}{4}$ ; the 3 in 12 cancels.
Truncating instead of rounding. $\frac{2}{3}$ rounded to two places is 0.67, not 0.66.

Convert the next fraction on your worksheet by hand first, then scan it in AI Math Tutor and check your division against its steps.

AI Math Tutor is a study aid, not a substitute for a teacher, and it can make mistakes: check every step, not just the answer.

Questions

How do you convert a fraction to a decimal?