What are all the fractions from 1/2 to 1/12 as decimals?

Here are the key values: 1/2 = 0.5, 1/3 = 0.333..., 1/4 = 0.25, 1/5 = 0.2, 1/6 = 0.1666..., 1/7 = 0.142857..., 1/8 = 0.125, 1/9 = 0.111..., 1/10 = 0.1, 1/11 = 0.0909..., and 1/12 = 0.0833... The ones with denominators that factor only into 2s and 5s (like 4, 5, 8, 10) produce terminating decimals; the rest repeat.

How do you know if a fraction will be a terminating or repeating decimal?

Simplify the fraction fully, then look at the denominator. If the denominator's only prime factors are 2 and/or 5, the decimal terminates. For example, 8 = 2³, so any fraction with denominator 8 terminates. If the denominator has any other prime factor (like 3, 7, or 11), the decimal repeats.

What is 1/3 as a decimal?

$\frac{1}{3} = 0.\overline{3}$, which means 0.3333... continuing forever. This is a repeating decimal. When rounding, you might write it as approximately 0.333 or 0.33 depending on the precision needed.

Fraction to Decimal Chart — Definition, Formula & Examples

A fraction to decimal chart is a reference table that shows the decimal equivalent of common fractions, such as 1/2 = 0.5, 1/4 = 0.25, and 1/3 = 0.333... You use it to quickly look up conversions instead of calculating them each time.

A fraction to decimal chart is a structured listing of rational numbers expressed simultaneously in fractional notation $\frac{a}{b}$ and their corresponding decimal representations obtained by dividing the numerator by the denominator. The chart typically includes fractions with denominators of 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 16, covering both terminating decimals (like $\frac{3}{8} = 0.375$ ) and repeating decimals (like $\frac{1}{6} = 0.1\overline{6}$ ).

Key Formula

\frac{a}{b} = a \div b

Where:

$a$ = The numerator (top number of the fraction)
$b$ = The denominator (bottom number of the fraction), where b ≠ 0

How It Works

To convert any fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example,

\frac{3}{4}

means

3 \div 4 = 0.75

. Some fractions produce terminating decimals that end after a few digits, while others produce repeating decimals that go on forever in a pattern. In a chart, repeating decimals are shown with a bar over the repeating digits, like

0.\overline{3}

for

\frac{1}{3}

. The chart below covers the most frequently used fractions organized by denominator, so you can find any common conversion in seconds.

Worked Example

Problem: Convert 7/8 to a decimal using long division.

Step 1: Set up the division: 7 divided by 8. Since 8 does not go into 7, place a decimal point and add zeros.

7.000 \div 8

Step 2: 8 goes into 70 eight times (8 × 8 = 64). Write 8 after the decimal point. Subtract to get a remainder of 6.

70 - 64 = 6

Step 3: Bring down the next 0 to make 60. 8 goes into 60 seven times (8 × 7 = 56). Subtract to get a remainder of 4.

60 - 56 = 4

Step 4: Bring down the next 0 to make 40. 8 goes into 40 exactly 5 times (8 × 5 = 40). The remainder is 0, so the division terminates.

40 - 40 = 0

Answer:

\frac{7}{8} = 0.875

Another Example

This example demonstrates a repeating decimal, unlike the first example which terminated. It shows how to recognize and notate a repeating pattern.

Problem: Convert 5/6 to a decimal.

Step 1: Divide 5 by 6. Since 6 does not go into 5, add a decimal point and zeros.

5.000... \div 6

Step 2: 6 goes into 50 eight times (6 × 8 = 48). Remainder is 2.

50 - 48 = 2

Step 3: Bring down a 0 to make 20. 6 goes into 20 three times (6 × 3 = 18). Remainder is 2 again.

20 - 18 = 2

Step 4: The remainder of 2 repeats, so the digit 3 will repeat forever. Use a bar to show the repeating part.

\frac{5}{6} = 0.8\overline{3}

Answer:

\frac{5}{6} = 0.8\overline{3}

(the 3 repeats infinitely)

Visualization

Why It Matters

Fraction-to-decimal conversions appear constantly in pre-algebra, algebra, and standardized tests like the SAT and GED. Carpenters, machinists, and cooks regularly switch between fractions and decimals when measuring. Having a mental chart of common equivalents speeds up estimation, mental math, and checking calculator results.

Common Mistakes

Mistake: Dividing the denominator by the numerator instead of numerator by denominator

Correction: Always divide the top number by the bottom number. For 3/4, compute 3 ÷ 4 = 0.75, not 4 ÷ 3 = 1.333...

Mistake: Rounding a repeating decimal too early and calling it exact

Correction: Writing 1/3 = 0.33 is only an approximation. The exact decimal is 0.333... (repeating). Use the overline notation

0.\overline{3}

when an exact answer is needed.

Mistake: Forgetting to simplify the fraction first, making the division harder

Correction: Simplify before dividing. Converting 6/8 is easier if you first reduce it to 3/4, then divide 3 ÷ 4 = 0.75.

Check Your Understanding

What is

\frac{5}{8}

as a decimal?

Hint: Divide 5 by 8 using long division, or note that 5/8 = (5 × 125)/(8 × 125) = 625/1000.

Answer: 0.625

Will

\frac{3}{7}

be a terminating or repeating decimal?

Hint: Check the prime factors of the denominator after simplifying.

Answer: Repeating, because 7 is not a factor of 2 or 5.

What is

\frac{2}{5}

as a decimal?

Hint: Divide 2 by 5, or multiply numerator and denominator by 2 to get 4/10.

Answer: 0.4

Related Terms

Fraction — The starting form being converted to a decimal
Decimal — The resulting form after conversion
Numerator — The top number you divide in the conversion
Denominator — The bottom number you divide by
Proper Fraction — Converts to a decimal less than 1
Improper Fraction — Converts to a decimal greater than or equal to 1
Mixed Number — Convert the fractional part to a decimal, add to the whole number
Fraction Rules — Rules for simplifying fractions before converting
Least Common Denominator — Useful when comparing fraction-to-decimal values
Ratio — Ratios can be expressed as fractions and then as decimals