CALCULATE WITH CONFIDENCE

Number Fundamentals & Precision

Reciprocal Calculator

Find a nonzero decimal's normalized exact multiplicative inverse.

Exact arithmetic

Find the multiplicative inverse

Exact fraction
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Exact reciprocal

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Understand the subject

What is a reciprocal?

A reciprocal is the number that multiplies with the original value to make one.

Use reciprocals to reverse rates, divide by a quantity, or change between a fraction and its inverse.

The key rule

What stays true

See the idea

Visual explanation

Example

Apply it

1 ÷ 0.125 = 8

Zero has no reciprocal because division by zero is undefined.

Quick guide

How to use this calculator

  1. Enter a nonzero finite decimal.
  2. Read the reduced exact fraction.
  3. Treat a capped decimal as a preview, not the exact answer.

Calculation method

Swap numerator and denominator

A decimal is first represented as an integer over a power of ten. Its reciprocal swaps those components and reduces the fraction.

Worked example

Reciprocal of 0.125

0.125 is 1/8, so its reciprocal is 8.

1 ÷ 0.125 = 8

Supported inputs

Precision and limits

Exact decimal input

Finite decimals use integer-scaled arithmetic, with no binary floating-point conversion.

Input boundary

Unless stated otherwise, use at most 200 digits total and 100 digits after the decimal marker.

Zero

Zero has no reciprocal because division by zero is undefined.