How this calculator works
The reciprocal of a number is 1 divided by that number, which swaps the numerator and denominator of a fraction. A whole number n becomes 1/n; a decimal is first written as an exact fraction from its digits and then inverted. Negative numbers keep their sign: the reciprocal of -2/5 is -5/2. Zero is excluded because it has no reciprocal.
Formula
For a nonzero number x, the reciprocal is 1/x. In fraction form, the reciprocal of a/b is b/a. A number times its reciprocal always equals 1.
Worked example
The reciprocal of 0.75 is 1/0.75 = 4/3, which is about 1.3333. The reciprocal of -1 1/2 is -2/3, because -1 1/2 = -3/2 and its fraction is flipped with the sign kept.
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Frequently asked questions
How do I find the reciprocal of a mixed number?
Convert it to an improper fraction first. For 2 3/4, multiply 2 by 4 and add 3 to get 11/4, then flip it to 4/11. This calculator does that conversion from the decimal value you enter.
What is the reciprocal of 1?
1, because 1 × 1 = 1. Every other number changes when inverted.
Can every decimal be inverted exactly?
Every terminating decimal is a fraction with a power of ten in the denominator, so its reciprocal is exact. Repeating decimals and irrational numbers also have reciprocals, but they may not have a short fraction form.
What is the difference between a reciprocal and an opposite?
The opposite changes the sign and adds to zero: the opposite of 3 is -3, and 3 + (-3) = 0. The reciprocal inverts the value and multiplies to one: the reciprocal of 3 is 1/3, and 3 × 1/3 = 1.