Fraction to Decimal Chart

88 fractions · denominators 2 to 32 · exact values

Every proper fraction you are likely to meet, with its decimal, whether that decimal terminates, and its percentage. The "behaviour" column is the useful one: it tells you at a glance whether a written decimal is the exact value or just the first few digits of a repeating one.

Fractions with denominator 2

Fraction	Decimal	Behaviour	Percent
1/2	`0.5`	terminates	50.00%

Fractions with denominator 3

Fraction	Decimal	Behaviour	Percent
1/3	`0.33333333…`	period 1	33.33%
2/3	`0.66666666…`	period 1	66.67%

Fractions with denominator 4

Fraction	Decimal	Behaviour	Percent
1/4	`0.25`	terminates	25.00%
2/4	`0.5`	terminates	50.00%
3/4	`0.75`	terminates	75.00%

Fractions with denominator 5

Fraction	Decimal	Behaviour	Percent
1/5	`0.2`	terminates	20.00%
2/5	`0.4`	terminates	40.00%
3/5	`0.6`	terminates	60.00%
4/5	`0.8`	terminates	80.00%

Fractions with denominator 6

Fraction	Decimal	Behaviour	Percent
1/6	`0.16666666…`	period 1	16.67%
2/6	`0.33333333…`	period 1	33.33%
3/6	`0.5`	terminates	50.00%
4/6	`0.66666666…`	period 1	66.67%
5/6	`0.83333333…`	period 1	83.33%

Fractions with denominator 8

Fraction	Decimal	Behaviour	Percent
1/8	`0.125`	terminates	12.50%
2/8	`0.25`	terminates	25.00%
3/8	`0.375`	terminates	37.50%
4/8	`0.5`	terminates	50.00%
5/8	`0.625`	terminates	62.50%
6/8	`0.75`	terminates	75.00%
7/8	`0.875`	terminates	87.50%

Fractions with denominator 10

Fraction	Decimal	Behaviour	Percent
1/10	`0.1`	terminates	10.00%
2/10	`0.2`	terminates	20.00%
3/10	`0.3`	terminates	30.00%
4/10	`0.4`	terminates	40.00%
5/10	`0.5`	terminates	50.00%
6/10	`0.6`	terminates	60.00%
7/10	`0.7`	terminates	70.00%
8/10	`0.8`	terminates	80.00%
9/10	`0.9`	terminates	90.00%

Fractions with denominator 12

Fraction	Decimal	Behaviour	Percent
1/12	`0.08333333…`	period 1	8.33%
2/12	`0.16666666…`	period 1	16.67%
3/12	`0.25`	terminates	25.00%
4/12	`0.33333333…`	period 1	33.33%
5/12	`0.41666666…`	period 1	41.67%
6/12	`0.5`	terminates	50.00%
7/12	`0.58333333…`	period 1	58.33%
8/12	`0.66666666…`	period 1	66.67%
9/12	`0.75`	terminates	75.00%
10/12	`0.83333333…`	period 1	83.33%
11/12	`0.91666666…`	period 1	91.67%

Fractions with denominator 16

Fraction	Decimal	Behaviour	Percent
1/16	`0.0625`	terminates	6.25%
2/16	`0.125`	terminates	12.50%
3/16	`0.1875`	terminates	18.75%
4/16	`0.25`	terminates	25.00%
5/16	`0.3125`	terminates	31.25%
6/16	`0.375`	terminates	37.50%
7/16	`0.4375`	terminates	43.75%
8/16	`0.5`	terminates	50.00%
9/16	`0.5625`	terminates	56.25%
10/16	`0.625`	terminates	62.50%
11/16	`0.6875`	terminates	68.75%
12/16	`0.75`	terminates	75.00%
13/16	`0.8125`	terminates	81.25%
14/16	`0.875`	terminates	87.50%
15/16	`0.9375`	terminates	93.75%

Fractions with denominator 32

Fraction	Decimal	Behaviour	Percent
1/32	`0.03125`	terminates	3.13%
2/32	`0.0625`	terminates	6.25%
3/32	`0.09375`	terminates	9.38%
4/32	`0.125`	terminates	12.50%
5/32	`0.15625`	terminates	15.63%
6/32	`0.1875`	terminates	18.75%
7/32	`0.21875`	terminates	21.88%
8/32	`0.25`	terminates	25.00%
9/32	`0.28125`	terminates	28.13%
10/32	`0.3125`	terminates	31.25%
11/32	`0.34375`	terminates	34.38%
12/32	`0.375`	terminates	37.50%
13/32	`0.40625`	terminates	40.63%
14/32	`0.4375`	terminates	43.75%
15/32	`0.46875`	terminates	46.88%
16/32	`0.5`	terminates	50.00%
17/32	`0.53125`	terminates	53.13%
18/32	`0.5625`	terminates	56.25%
19/32	`0.59375`	terminates	59.38%
20/32	`0.625`	terminates	62.50%
21/32	`0.65625`	terminates	65.63%
22/32	`0.6875`	terminates	68.75%
23/32	`0.71875`	terminates	71.88%
24/32	`0.75`	terminates	75.00%
25/32	`0.78125`	terminates	78.13%
26/32	`0.8125`	terminates	81.25%
27/32	`0.84375`	terminates	84.38%
28/32	`0.875`	terminates	87.50%
29/32	`0.90625`	terminates	90.63%
30/32	`0.9375`	terminates	93.75%
31/32	`0.96875`	terminates	96.88%

Chart notes

Which denominators always terminate?

Those whose prime factors are only 2 and 5 — 2, 4, 5, 8, 10, 16, 20, 25, 32 and so on. Anything with a 3, 7, 11 or other prime in it recurs, however the numerator is chosen.

How long can a repeating block get?

At most one less than the denominator once the 2s and 5s are removed. Thirds repeat a single digit, sevenths repeat six, and the maximum grows quickly with the size of the prime involved.

Is a rounded decimal ever exactly right?

Only when the fraction terminates. For a recurring decimal any finite string is an approximation, which is why the exact form stays as a fraction in arithmetic that needs precision.