Decimal to Fraction Calculator

How do you convert a decimal to a fraction by hand?

Write the digits over a power of ten, one zero per decimal place: 0.625 has 3 places, so 625/1000. Find the GCD of 625 and 1000, which is 125, and divide both by it to get 5/8. The tool shows these as its raw fraction, GCD and simplified steps.

Is there a limit on how many decimal places it handles?

The only limit is the 15 to 17 significant digits a typed number can carry. The tool reads the digits of the shortest decimal form and does the arithmetic with exact big integers, so 0.333333333333 returns 333333333333/1000000000000. Entered as 0.1 + 0.2, the stored value 0.30000000000000004 becomes 7500000000000001/25000000000000000.

Does it recognise 0.3333 as 1/3?

No. It converts exactly what you type, so 0.3333 returns 3333/10000 and 0.142857 returns 142857/1000000. There is no search for a nearby simple fraction and no denominator cap. To get 1/3 exactly, use the algebra x = 0.333…, 10x − x = 3.

How are negative numbers, zero and whole numbers shown?

The minus sign sits on the numerator, so −0.75 gives −3/4 and −2.5 gives −5/2 with the mixed number −2 1/2. Zero returns 0/1, and a whole number such as 4 returns 4/1 with no mixed-number row. A cleared box is treated as zero.

What does the mixed number row show?

It appears when the magnitude is at least 1 and the fraction is not a whole number. 2.375 simplifies to 19/8 and appears as 2 3/8, since 19 − 2 × 8 = 3. Numbers below 1 do not get the row.

What happens with very small or very large numbers?

Numbers that JavaScript writes in exponent form, such as 1e-7 or 1e21, are expanded correctly. 1e-7 returns 1/10000000. Earlier, 1e-7 returned 0/1 because the exponent form has no decimal point to count.

What is the decimal verification row?

It divides the simplified numerator by the denominator and shows the result to 12 significant digits with trailing zeros removed. For 5/8 it prints 0.625. It confirms the fraction matches the input to that precision, nothing more.

Can irrational or repeating decimals be converted exactly?

Only the finite digits you type are converted. Repeating decimals are rational but need algebra, and irrational numbers such as π have no fraction at all, so entering 3.14159 returns 314159/100000, which is not π.