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Decimals as fractions

The answer is the least interesting part. 0.375 is 375/1000 before it is 3/8, and the step between them — divide both by 125, their greatest common divisor — is what the question is actually about. Every page here shows it, and says outright when a decimal will not reduce.

The reduction, not just the result

Both forms are printed: the digits over their place value, and what divided into both. 0.37 stays 37/100 because 37 is prime.

Repeating decimals get the algebra

10x minus x cancels the tail exactly, so 0.333… is 3/9 and then a third. No rounding anywhere in it.

And the tape-measure answer

The nearest sixteenth, with how far off it is in millimeters, because a decimal off a caliper usually has to become a mark.

Repeating decimals

The cases a rounded answer gets wrong. A third is not 333/1000, and each of these shows the subtraction that cancels the endless tail.

Sixteenths, off a tape or a caliper

The decimals that land exactly on a mark. These are the ones that reduce dramatically — 0.375 is 375/1000 before it is 3/8.

Hundredths, 0.01 to 0.49

Half of these will not reduce at all, and the page says which and why.

Hundredths, 0.50 to 0.99

Above one

Shown both as an improper fraction and as a mixed number.

Above four

The rest of the family, up to 9.9.

Any decimal at all

These pages are built from two calculators that take any numbers: simplify a fraction and fraction to decimal.