Reciprocal Table (1/x)

The reciprocal table (also called an inverse table) lists the values of 1/x for a range of numbers. It is a classic reference for fast division, calculation checks, and numerical approximation in math, science, and engineering.

What Is a Reciprocal?

The reciprocal of a real number x (where x ≠ 0) is the value that multiplies by x to equal 1:

reciprocal(x) = 1 / x

Examples

If x = 2, then 1/x = 0.5.
If x = 4, then 1/x = 0.25.
If x = 0.1, then 1/x = 10.

Note: The reciprocal of 0 does not exist because division by zero is undefined.

Why Use a Reciprocal Table?

Reciprocal tables are useful for:

Fast division: dividing by x is the same as multiplying by 1/x.
Checking calculations and reducing arithmetic errors.
Engineering and physics problems with inverse relationships.
Electrical engineering (e.g., relationships proportional to 1/R).
Quick estimates and mental math.

How to Use the Table

Find the value of x in the table.
Read the corresponding value of 1/x.
To compute A ÷ x, calculate A × (1/x).

Example 1

Compute 18 ÷ 6 using reciprocals:
1/6 = 0.166666… and 18 × 0.166666… ≈ 3.

Example 2

Compute 75 ÷ 8:
1/8 = 0.125 → 75 × 0.125 = 9.375.

Precision and Rounding

Many reciprocals are repeating decimals (for example, 1/3 = 0.333…). For that reason, tables usually display values rounded to a fixed number of decimal places.

6 decimals is a common balance between readability and accuracy.
8-10 decimals may be better for technical applications.
For large x, scientific notation can be useful (e.g., 1/5000 = 2e-4).

Tip: If the table is mainly for quick reference, 6 decimals is typically enough. For higher-precision workflows, consider 8-10 decimals.

Reciprocal Table (1-50)

The table below lists 1/x for integers from 1 to 50, rounded to 6 decimal places.

x	1/x	x	1/x
1	1.000000	26	0.038462
2	0.500000	27	0.037037
3	0.333333	28	0.035714
4	0.250000	29	0.034483
5	0.200000	30	0.033333
6	0.166667	31	0.032258
7	0.142857	32	0.031250
8	0.125000	33	0.030303
9	0.111111	34	0.029412
10	0.100000	35	0.028571
11	0.090909	36	0.027778
12	0.083333	37	0.027027
13	0.076923	38	0.026316
14	0.071429	39	0.025641
15	0.066667	40	0.025000
16	0.062500	41	0.024390
17	0.058824	42	0.023810
18	0.055556	43	0.023256
19	0.052632	44	0.022727
20	0.050000	45	0.022222
21	0.047619	46	0.021739
22	0.045455	47	0.021277
23	0.043478	48	0.020833
24	0.041667	49	0.020408
25	0.040000	50	0.020000

Common Mistakes

Reciprocal vs. opposite: the opposite of x is -x, not 1/x.
Trying to compute 1/0: it is undefined.
Over-rounding: it can introduce noticeable error in multi-step calculations.

Frequently Asked Questions

Is the reciprocal of a negative number also negative?

Yes. For example, 1/(-4) = -0.25.

What is the reciprocal of a fraction?

If you have a/b, its reciprocal is b/a (as long as a ≠ 0). Example: the reciprocal of 2/5 is 5/2.

Why do some reciprocal values never end?

Because some fractions produce repeating decimals, such as 1/3 = 0.333…. A table shows rounded approximations.