Antilogarithm Calculator

The Antilogarithm Calculator will calculate:

1. The antilogarithm of a number.
2. The antilogarithm of a number rounded to the correct number of significant figures determined by the input.
3. The antilogarithm of a number rounded to the correct number of decimal places as determined by user input (default is 4 decimla places).

Antilogarithm Calculator Parameters: Antilogarithm cannot be negative;

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each antilogarithm calculation, the Antilogarithm Calculator will automatically calculate the results and update the formula elements with each element of the antilogarithm calculation. You can then email or print this antilogarithm calculation as required for later use.

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Theoretical description

If log A = x, then A is called the antilogarithm of x and is written as A = antilog x.

For example, if log 1000 = 3 (because 10³ = 1000), then antilog 3 = 1000. In simpler words, the term "antilogarithm" is an alternative version of "10 in power ".

If A is negative, the value of antilogarithm is smaller than 10 but it is always positive anyway. For example, antilog (-2) = 0.01 because 10^-2 = 1 / 100 = 0.01.

The value of antilogarithm is not always that simple. If we have to find the antilogarithm of a decimal number, the result may be a real number with an infinite number of decimal places. Therefore, we may need to round the result to a certain number of decimal places. However, this may cause confusion, as different users may round the result to different decimal places. Hence, it is useful to appoint some rules in rounding such numbers. The most suitable rule in this regard is to express the result in the same number of significant figures as the antilogarithm input.

For example, if we have to calculate antilog 5.32, we must express the result in 3 significant figures because 5.32 has 3 s.f. We have

Since the result is a real number with an infinite number of digits after the decimal place, we have to round the answer to 3 significant figure to fit the input. Hence, based on the rounding rules and those of significant figures, we obtain

where only the first three digits are significant, as this is a whole number and trailing zeroes are not significant.

This approach is also used in negative numbers. For example,

However, we cannot write the result in this way. Since -3.147 has four significant figures, we must write the result accordingly (leading zeroes are not significant). Hence, applying the known rounding rules, we obtain

This is because the digit on the right of 8 is 5 (5 > 4), so 8 becomes 9.